\(2^6 = 64\) subsets. We need to select yes/no for each of the six elements.
\(2^3 = 8\) subsets. We need to select yes/no for each of the remaining three elements.
\(2^6 - 2^3 = 56\) subsets. There are 8 subsets which do not contain any odd numbers (select yes/no for each even number).
\(3\cdot 2^3 = 24\) subsets. First pick the even number. Then say yes or no to each of the odd numbers.