In order to factorise $x^{2}+9 x+18,$ we have to find two numbers $p$ and $q$ such that $p+q=9$ and $p q=18.$

Clearly, $6+3=9$ and $6 \times 3=18.$

So, we write the middle term $9 x$ as $6 x +3$.

$\therefore$ $x^{2}+9 x+18=x^{2}+6 x+3 x+18$

$=x(x+6)+3(x+6)$

$=(x+6)(x+3)$