A. If you use 2 quarters, you have to make the remaining 15¢ with either no
dimes or 1 dime and the rest in nickels.

That's 2 ways.

B. If you use 1 quarter, you have to make the remaining 40¢ with either no
dimes, 1 dime, 2 dimes, 3 dimes or 4 dimes and the rest, if any, in nickels.

That's 5 more ways.  

C. If you don't use any quarters, you have to make the entire 65¢ with either
0, 1, 2, 3, 4, 5 or 6 dimes and the rest in nickels.

That's 7 more ways.  2+5+7 = 14 ways in all.

Edwin