\[3x^{2} - 48xy + 192y^{2} =\]
\[= 3 \cdot \left( x^{2} - 16xy + 64y^{2} \right) =\]
\[= 3 \cdot (x - 8y)^{2} =\]
\[= 3 \cdot (x - 8y)(x + 8y)\]