Simplifying
4x2y + 12xy2 + 9y3

Reorder the terms:
12xy2 + 4x2y + 9y3

Factor out the Greatest Common Factor (GCF), 'y'.
y(12xy + 4x2 + 9y2)

Factor a trinomial.
y((2x + 3y)(2x + 3y))

Final result:
y(2x + 3y)(2x + 3y)