Let the required volume of the solution B be X quarts

As we know, 3 quarts of solution A containing $\(5 \%\)$ of hydrogen peroxide when mixed with X quarts of solution B containing $\(20 \%\)$ of hydrogen peroxide results in a solution containing $\(15 \%\)$ of hydrogen peroxide, so we

get $\(5 \% \times 3+20 \% \times X=15 \% \times(3+X) \Rightarrow X=6\)$ quarts

Hence the volume of solution B required is 6 quarts, so the answer is (D).