Factoring by Grouping
2ax + 3bx + 8ay + 12by = (x+4y) (2a+3b)
First, group terms with common variables.
(2ax + 3bx) + (8ay + 12by)
Factor each using GCMF or greatest common monomial factor
x(2a + 3b) + 4y (2a + 3b)
Lastly, simplify it. In this case, we can simply copy one (2a + 3b) then combine their common factors which are x and 4y.
(x + 4y) (2a + 3b)