\[(x + 3)^{2} - (x - 3)^{2} =\]
\[= \left( x + 3 - (x - 3) \right)(x + 3 + x - 3) =\]
\[= (x + 3 - x + 3) \cdot 2x =\]
\[= 6 \cdot 2x = 12x.\]