Factor completely:x2 – 4xy + 12ax – 48ay?

assuming you meant x^2

just use the "grouping in pairs" technique
factorise x out of the first pair, and 12 a out of the second pair since x highest common factor in x^2-4xy, as 12a is in 12ax-48ay
we end up, x(x-4y)+12a(x-4y), and since (x-4y) is a common factor in both we can factorise that as (x+12a)(x-4y)
so:

x(x-4y)+12a(x-4y)
(x+12a)(x-4y)

= x² - 4xy + 12ax - 48ay
= x(x - 4y) + 12a(x - 4y)
= (x + 12a)(x - 4y)

Answer: (x + 12a)(x - 4y)

Proof (F.O.I.L.):
= (x + 12a)(x - 4y)
= x² - 4xy + 12ax - 48ay

x^2 - 4xy + 12ax - 48ay
= (x^2 - 4xy) + (12ax - 48ay)
= x(x - 4y) + 12a(x - 4y)
= (x - 4y)(x + 12a)

x (x - 4y) + 12 a (x - 4y)
(x - 4y) (x + 12 a)