Answer
$2x(3x+4y)^2$
Work Step by Step
The product of a binomial sum and a binomial difference is: $(A+B)(A-B)=A^2-B^2$.
The square of a binomial sum is: $(A+B)^2=A^2+2AB+B^2$.
The square of a binomial difference is: $(A-B)^2=A^2-2AB+B^2$.
Hence here: $18x^3+48x^2y+32xy^2=\\=2x(9x^2+24xy+16y^2)\\=2x((3x)^2+2\cdot3x\cdot4y+(4y)^2\\=2x(3x+4y)^2$