2. 1. The definition of the absolute value function is y = x if x is nonnegative, and y = -x if x is negative. So in order to evaluate $|2(x+1)| = |2x + 2|$, you put in the value for x, and then if $2x + 2 \geq 0$, the value stays unchanged; otherwise, it becomes positive. For example, if x = 0, then $2x + 2 = 2(0) + 2 = 2$, so $|2x + 2| = |2| = 2$. If x = -3, then $2x + 2 = 2(-3) + 2 = -4$, and $|2x + 2| = |-4| = 4$.
2. After you evaluate $(.5(x+2))^2 = .25(x+2)^2$, you see that $a = -0.25$. I'm not sure what you are asking here, though.