\[(a - b + 4)(a - b - 4) =\]
\[= \left( (a - b) + 4 \right)\left( (a - b) - 4 \right) =\]
\[= (a - b)^{2} - 4^{2} =\]
\[= a^{2} - 2ab + b^{2} - 16.\]