I am trying to review through self-study, but am having difficulty factoring this expression (despite having some help).

The Expression:

2x^2(x+3) + 4x(x+3)^2

Their method of factoring is as follows:

2x(x+3)[x+2(x+3)]

= 2x(x+3)(3x+6)

= 2x(x+3)3(x+2)

= 6x(x+3)(x+2)

Any suggestions or links I can follow? Any help would be greatly appreciated.