Answer
$3(a+b)(a+6b)$
Work Step by Step
$ 3a^{2}+15ab+18b^{2}\qquad$... factor out the common term, $3$
$=3(a^{2}+5ab+6b^{2})$
... Searching for two factors of $ac=6$ whose sum is $b=5,$
we find$\qquad 1$ and $6.$
Rewrite the middle term and factor in pairs:
$=3(a^{2}+ab+6ab+6b^{2})=$
$=3[a(a+b)+6b(a+b)]$
= $3(a+b)(a+6b)$
