2x² - 8 - (x + 2)(-2x + 6)

2(x² - 4) - (x + 2)(-2x + 6)

Factorise x² - 4 as (x - 2)(x + 2)

Factorise -2x + 6 as -2(x - 3)

2(x - 2)(x + 2) - (x + 2)[-2(x - 3)]

2(x - 2)(x + 2) + 2(x + 2)(x - 3) 

2(x + 2) is a common factor of bath as you see by the red coloring:

2(x - 2)(x + 2) + 2(x + 2)(x - 3)

2(x + 2)[(x - 2) + (x - 3)]

2(x + 2)[x - 2 + x - 3]

2(x + 2)(2x - 5)

Without the red coloring:

2(x + 2)(2x - 5)

Edwin