The only correct choice is (a) 

There is no way to have 15 cents with 4 coins.

You obviously can't use pennies or quarters.

If you use a dime, you'd have to have the remaining 5 cents with 3 coins,
and that's impossible.

If you use a nickel, you'd have to have the remaining 10 cents with 3 coins,
and that's also impossible.

All the others are possible:

3 nickels and 1 dime equals 25 cents.
1 nickel and 3 dimes equals 35 cents.
2 nickels, 1 dime, and 1 quarter equals 45 cents.
3 dimes and 1 quarter equals 55 cents.

Edwin