\[(2y - 2c)(3y - 3c) =\]
\[= 2 \cdot 3 \cdot (y - c)(y - c) =\]
\[= 6 \cdot (y - c)^{2} =\]
\[= 6 \cdot \left( y^{2} - 2yc + c^{2} \right) =\]
\[= 6y^{2} - 12yc + 6c^{2}\text{.\ }\]