4(x-6)< -2x+6 what is the solution to the inequality _

Simplify both sides if needed. The left-hand side needs simplification.

4(x - 6)  -2x + 6
4x - 24   -2x + 6

All is left to do is add and subtract to get the x variable all alone.

4x - 24   -2x + 6
6x - 24    6    <-- Add 2x to both sides
6x           30  <-- Add 24 to both sides 
x            5    <-- Divide both sides by 6

In order to be in the solution set, x has to be less than or equal to 5.

In interval notation: [5, -∞)