How do you factor by grouping 6a+12b+18c?

You cannot factor this expression by grouping because none of the variables is the same. You can factor out $6$.
$6 a + 12 b + 18 c$ =
$6 \left(a + 2 b + 3 c\right)$
A trinomial to be factored by grouping has the generic form of $a {x}^{2} + b x + c$, where $c$ is a constant. For example, $5 {x}^{2} + 11 x + 2$.