\[3x^{2} - 24xy + 48y^{2} =\]
\[= 3 \cdot \left( x^{2} - 8xy + 16y^{2} \right) =\]
\[= 3 \cdot (x - 4y)^{2} =\]
\[= 3 \cdot (x - 4y)(x - 4y)\]