Answer: "Extending Axis and shortening British lines" means that the intervention in Greece, which was referred to in the context of this statement, was a delaying action that had the effect of extending the lines of the Axis powers (Germany, Italy, and Japan) and shortening the lines of the British forces.
In military terms, "lines" refer to the front lines of a battle, or the positions where opposing forces are engaged in combat. The longer the front lines, the more difficult it is for a military force to defend its positions, because it must spread its resources more thinly. By contrast, shortening lines can make it easier to defend a position.
Therefore, extending the lines of the Axis powers and shortening the lines of the British forces would have made it more challenging for the British to defend their positions and would have given the Axis powers an advantage in the conflict. However, President Roosevelt considered this action to be "wholly justifiable" because it would delay the Axis advance and give the British more time to prepare for the coming battles.
Explanation: "Extending Axis and shortening British lines" is a military strategy that refers to the idea that by diverting British military resources to defend Greece, the Axis powers (Germany, Italy, and Japan) would be able to stretch the British defenses thin and make it easier to defeat them. Essentially, the Axis powers would be able to extend their own lines of defense while shortening the British lines, making it easier for them to attack and conquer British territories. The message from Roosevelt to Churchill is acknowledging that the intervention in Greece was a necessary action to delay the Axis advance and prevent them from gaining further territory, even though it would also have the effect of weakening British defenses in other areas.