eddy2017, you are taking the square root of both sides.
√(x+6)^2 = √4 \(\displaystyle \ \ \ \ \ \ \ \) <----- This is a correct step. It is equivalent to:
|x + 6| = 2 \(\displaystyle \ \ \ \ \ \ \ \ \) <----- That leads to:
x + 6 = ±2 \(\displaystyle \ \ \ \ \ \ \ \) <----- That can be read as "x plus 6 equals positive or negative 2."
x = -6 ± 2 \(\displaystyle \ \ \ \ \ \ \ \ \) <----- That can be read as "x equals negative 6 plus or minus 2."
x = -6 - 2 \(\displaystyle \ \ \) or \(\displaystyle \ \ \) x = -6 + 2
x = -8 \(\displaystyle \ \ \) or \(\displaystyle \ \ \) x = -4
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