Force concentration
With the attacking force having only two armoured units, the defenders should have the advantage.
However, as the defensive line increases from the imaginary four units in length, the advantage slips from the defender to the attacker. The longer the line to be held, the thinner the defenders will be spread. With the defender having sacrificed his mobility to dig in, the attacker can choose where and when to attack. Either penetrating the line or turning a flank and thus being able to destroy the enemy in detail. Thus, concentrating two divisions and attacking at a single point generates a far greater force than is achieved by spreading two divisions into a line and pushing forward on a broad front.
Concentration of force in this scenario requires mobility (to permit rapid concentration) and power (to be effective in combat once concentrated). The tank embodies these two properties and for the past seventy years has been seen as the primary weapon of conventional warfare.
No one side has a monopoly on military art, and what is obvious to one side is obvious to the other. A far more likely scenario is that both forces will choose to use their infantry to hold a line and to concentrate their armour, and rather than a line in the sand, the infantry line would be more of a trip wire, to warn of where the enemy has chosen to launch his attack, with the armoured forces jostling to find the right place to attack or counterattack. Other considerations, then, must come into play for a decisive blow to be achieved.
Such considerations may be economic or political in nature, e.g. one side is unable or unwilling to allow the sanctity of its soil to be violated, and thus insists on defending a line on a map.

History: Force concentration has been a part of the military commander's repertoire since the dawn of warfare, though maybe not by that name. Commanders have always tried to have the advantage of numbers. The declined flank for example, was one way of achieving a force concentration during a battle.

Disposition of Roman Legions: At the beginning of the Roman Empire, in the first years of the first millennium, Rome's Legions were grouped into battle groups of three or four Legions, on the Rhine, on the Danube and in the Levant. By the third century A.D. these Legions had been dispersed along the frontiers in frontier fortifications, and within the Empire as internal security troops. In the first case Rome's military might was disposed in a manner in which it had a concentration of force capable of offensive action; in the second case it could defend effectively but could only attack and counterattack with difficulty.

Guerrilla warfare: As they are usually the smaller in number an appreciation of force concentration is especially important to guerrilla forces, who find it prudent initially to avoid confrontations with any large concentrations of government/occupying forces. However, through the use of small attacks, shows of strength, atrocities etc. in out of the way areas, they may be able to lure their opponents into spreading themselves out into isolated outposts, linked by convoys and patrols, in order to control territory. The guerrilla forces may then attempt to use force concentrations of their own; using unpredictable and unexpected concentrations of their forces, to destroy individual patrols, convoys and outposts. In this way they can hope to defeat their enemy in detail.
Regular forces, in turn, may act in order to invite such attacks by concentrations of enemy guerrillas, in order to bring an otherwise elusive enemy to battle, relying on its own superior training and firepower to win such battles. This was successfully practiced by the French during the First Indochina War at the Battle of Nà Sản, but a subsequent attempt to replicate this at Dien Bien Phu led to decisive defeat.

Aerial warfare: During World War I the Central Powers became increasingly unable to meet the Allied Powers in terms of outright number of fighter aircraft. To overcome this shortcoming rather than deploying their fighters uniformly along the fronts, the Germans concentrated their fighters into large mobile Jagdgeschwader formations, the most famous of which was Manfred von Richthofen's Flying Circus, that could be moved rapidly and unexpectedly to different points along the front. This allowed them to create a local superiority in numbers, that could achieve air supremacy in a local area in support of ground operations or just to destroy Allied fighters in the overall strategy of attrition.
Similarly the Second World War Big Wing was one tactic that was evolved to cause maximum damage to the enemy with the minimum of casualties.

Blitzkrieg: Modern armour warfare doctrine was developed and established during the run up to World War II. A fundamental key to conventional Warfare is the concentration of force at a particular point (the [der] Schwerpunkt). Concentration of force increases the chance of victory in a particular engagement. Correctly chosen and exploited, victory in a given engagement or a chain of small engagements is often sufficient to win the battle.

Defence of France 1944: The Nazi defence of France in 1944 could have followed one of the two models offered in the hypothetical example. The first was to distribute the available forces along  the Atlantic Wall and throw the invading Allies back into the sea where and when they landed. The second was to keep the German Panzers concentrated and well away from the beaches. Territory could then be conceded to draw the invasion force away from their lodgement areas from which it would be nipped off by the cutting of their supply lines and then defeated in detail. The superiority of concentrated forces using maneuver warfare in the hypothetical example carried the proviso of "all other things being equal"; by 1944 things were far from being equal.
With Allied air superiority not only were major force concentrations vulnerable to tactical and heavy bombers themselves, but so were the vital assets—bridges, marshalling yards, fuel depots, etc.—needed to give them mobility. As it was in this case, the blitzkrieg solution was the worst of both worlds,  neither being far enough forward to maximise the use of their defensive fortifications, nor far enough away and concentrated to give it room to manoeuvre.
Similarly, for the Japanese in the final stages of the Island hopping campaign of the Pacific War, with Allied naval and air superiority and non-existent room to manoeuvre, neither a water's edge defensive strategy nor a holding back and counterattacking strategy could succeed.

Cold War and beyond: For much of the Cold War, to combat the overwhelming Soviet supremacy in armour and men, NATO planned to use much of West German territory as a flood plain in a defence in depth to absorb and disperse the momentum of a massed Soviet attack. Mobile anti-tank teams and counterattacking NATO armies would seek to cut off the leading Soviet echelons from their supporting echelons and then reduce the isolated elements with superior air power and conventional munitions, and if this failed, with nuclear munitions.
In an effort to avoid the use of nuclear munitions in an otherwise conventional war, the US invested heavily in a family of technologies it called "Assault Breaker", the two parts of these programmes were an enhanced realtime intelligence, surveillance, target acquisition, and reconnaissance capability, and the second part a series of stand off precision guided air-launched and artillery weapon systems, such as the MLRS, ICMs, M712 Copperhead, and the BLU-108 submunition. Against such weapons massed concentrations of armour and troops would no longer be a virtue but a liability. From the mid eighties and onward a much greater level of force dispersal became desirable rather than concentration.

See also: 

References: 

Sources: Carl von Clausewitz, On War, online version available, especially Book 3, Chapter VIII ("Superiority of Numbers"), and Chapter XI ("Assembly of Forces in Space").
Dunnigan, James F. How To Make War, 2003, HarperCollins Publishers, New York.