\[(b + 4)b - (b + 2)^{2} =\]
\[= b^{2} + 4b - \left( b^{2} + 2 \cdot b \cdot 2 + 2^{2} \right) =\]
\[= b^{2} + 4b - b^{2} - 4b - 4 = - 4.\]