Factorize each of the following algebraic expressions:

$4(x+y)(3 a-b)+6(x+y)(2 b-3 a)$

$=2(x+y)[2(3 a-b)+3(2 b-3 a)] \quad\{$ Taking $[2(x+y)]$ as the common factor $\}$

$=2(x+y)(6 a-2 b+6 b-9 a)$

$=2(x+y)(4 b-3 a)$