We want to solve for x in:

`4(x - 6) = -2(x-3)`

This simply means isolating x. To do so, we first distribute the terms in both sides of the equation:

`4x - 24 = -2x + 6`

Then, we combine similar terms: constants on one side, those containing x on the other:

`4x + 2x = 6 + 24`

`6x = 30`

Then, we isolate xby dividing both sides by 6.

`(6x)/6 = 30/6`

`x = 5`

Therefore, x = 5.

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To check, we substitute 5 to x:

`4(5 -6) = -2(5-3)`

`4(-1) = -2(2)`

`-4=-4`

Since we arrived at a true statement, the answer is correct.