If you don't use any quarters, you can use 0 through 7 dimes 
and the rest in nickels.  That's 8 ways.

If you use 1 quarter, you can use 0 through 5 dimes, 
and the rest, if any, in nickels.  That's 6 ways. 
 
If you use 2 quarters, you can use 0 through 2 dimes,
and the rest in nickels.  That's 3 ways.

And finally you can use 3 quarters.  That 1 way.

Total = 8+6+3+1 = 18 ways.

Edwin