\[4a(a - 2) - (a - 4)^{2} =\]
\[= 4a^{2} - 8a - \ \left( a^{2} - 8a + 16 \right) =\]
\[= 4a^{2} - 8a - a^{2} + 8a - 16 =\]
\[= 3a^{2} - 16\]