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8x - 2(3x - 4 + 2y) - 12x

=8x + 2(-3x + 4 - 2y) - 12x

=8x  -6x + 8 - 4y - 12x

=8x  -6x - 12x + 8 - 4y 

= -10x + 8 - 4y 

Simplify the following:
8 x-2 (-4+3 x+2 y)-12 x

Grouping like terms, 8 x-2 (-4+3 x+2 y)-12 x = -2 (-4+3 x+2 y)+(8 x-12 x):
-2 (-4+3 x+2 y)+(8 x-12 x)

8 x-12 x = -4 x:
-4 x-2 (-4+3 x+2 y)

-2 (-4+3 x+2 y) = 8-6 x-4 y:
8-6 x-4 y-4 x

Grouping like terms, 8-6 x-4 y-4 x = -4 y+(-6 x-4 x)+8:
-4 y+(-6 x-4 x)+8

-6 x-4 x = -10 x:
-4 y+-10 x+8

Factor 2 out of -4 y-10 x+8:
Answer: | 
| 2 (-2 y-5 x+4)                     =  -10x -4y + 8