\[(4a + 4c)(a + c) =\]
\[= 4 \cdot (a + c)(a + c) =\]
\[= 4 \cdot (a + c)^{2} =\]
\[= 4 \cdot \left( a^{2} + 2ac + c^{2} \right) = \ \]
\[= 4a^{2} + 8ac + 4c^{2}\text{.\ }\]