$16 x^{2}+4 y^{2}+9 z^{2}-16 x y-12 y z+24 x$

$=(4 x)^{2}+(-2 y)^{2}+(3 z)^{2}+2(4 x)(-2 y)+2(-2 y)(3 z)+2(3 z)(4 x)$

$=\{4 x+(-2 y)+3 z\}^{2}\left[\because a^{2}+b^{2}+c^{2}+2 a b+2 b c+2 c a=(a+b+c)^{2}\right]$

$=(4 x-2 y+3 z)^{2}$

$=(4 x-2 y+3 z)(4 x-2 y+3 z)$