Answer
$ 2x(x+6-2a)(x+6+2a)$
Work Step by Step
$ 2x^{3}-8a^{2}x+24x^{2}+72x=\quad$... we have a common factor, $2x$
$=2x(x^{2}-4a^{2}+12x+36)$
the terms not containing $a$ form a recognizable trinomial
$=2x[(x^{2}+12x+36)-4a^{2}]$
$=2x[(x^{2}+2\cdot 6x+6^{2})-4a^{2}]$
... a square of a sum, $A^{2}+2AB+B^{2}=(A+B)^{2}$
$=2x[(x+6)^{2}-4a^{2}]$
... the brackets contain a difference of squares, $(x+6)^{2}-(2a)^{2}$
$=2x(x+6-2a)(x+6+2a)$
