If 15 cans of food are needed for 7 men for 2 days, the number of cans for 4 men for 7 days is

If 15 cans of food are needed for 7 men for 2 days, then 30 cans of food are needed for 4 men for 7 days. 

Assuming that the men eat every day, without skipping a day, then the first part of the sentence is basically saying 15 cans can feed 14 men. There are seven men who can survive off part of the 15 cans on day one, and seven men who can survive off of what's left of the 15 cans on day two.  The 15 cans have the potential to feed 14 men in one day basically. Applying this same theory, x number of cans has the potential to feed 28 (that's 4 men for 7 days). If these cans are the same size and are equal in terms of how filling its contents are, then we can set up a proportion.

15/14 = x/28
If 15 cans of food can feed 14 men, then x cans of food can feed 28 men.
Cross Multiply
14x = 420
Divide both sides by 14
x = 30

30 cans of food can feed 4 men for 7 days. Hope this helps!