Which of the following is the solution to 4|x+3|> 8?

Too bad you haven't shared illustrations of the possible solutions.

Starting with   4|x+3|>8, div. both sides by 4:     |x+3|>2

Case 1:  x+3 is already positive:  then x+3>2, or x > -1

Case 2:  x+3 is negative:  Then -(x+3)>2, or -x - 3 > 2, or -5>x or x<-5

Draw a number line representing x values.  Place empty circles at x = -5 and x = -1.  Draw a vector from the circle at x = -1, to the right of x = -1.  Draw a vector from the circle at x = - 5, to the left of x = -5.  Note that x values between x = -5 and x = -1 are not solutions.