2pq + 6p -6q - 18

Bring out the common terms.

6p = 2p x 3
18 = 3 x 6

2pq + 2p x 3 -6q - 3 x 6

2p(q + 3) - 6(q + 3)
(2p - 6)(q + 3)

Factorize (2p - 6) further

2p - 6
6 = 2 x 3
2p -3 x 2
2(p - 3)

(2p - 6)(q + 3) = 2(p - 3)(q + 3)

Group them and factorize like terms out

xy - xm - my + m²

x(y-m) - m(y - m)

NOTE

- x - = + and + = - x -

m² = -m x -m

x(y-m) - m(y - m)

(x - m)(y-m)

Let's group them

The 3ax + 6a Group

Bring out which numbers or letters are common in both expressions

You can see 3 can go into 6, hence 3 is common

a also appeared at both sides, hence a is also common

3a(x+2)

The - x - 2 Group

-x = -1 x x

-2 = -1 x 2

Hence - x - 2 = -1 x x -1 x 2

- 1 is common

-1 x x -1 x 2 = -1(x+2)

3ax + 6a - x - 2 = 3a(x+2)-1(x+2)

3a(x+2)-1(x+2)

(x+2) is also common, hence bring it out

(x+2)(3a-1)

(x+2)(3a-1) is the same as (3a-1)(x+2), you can change the order of multiplication and the result will still be the same