2. If there are $x$ black pieces, then there are $32-x$ white pieces. Since each black piece (pentagonal) borders only white pieces, the number of black and white piece borders will be $5 x$. On the other hand, such borders are $3 \cdot(32-x)$. From the equation $5 x=3 \cdot(32-x)$ we get $x=12$.
Answer: 12.

Answer to option: 5-2: 20.