Consider the following figure that shows the graph of the function $$F$$ defined by
$$F(x) = | 2x | + 4$$ for all numbers x:

For which of the following functions G defined for all numbers x does the graph of G intersect the graph of F?

F(x) = |2x| + 4

Option A: G(x) = x + 3

If x > 0 or x = 0

2x + 4 = x + 3

x = -1 < 0

Therefore, this case is not possible.

If x < 0

-2x + 4 = x + 3

3x = 1

x = 1/3 > 0

Therefore, this case is not possible.

Option B: G(x) = 2x - 2

If x > 0 or x = 0

2x + 4 = 2x - 2

This case is not possible.

If x < 0

-2x + 4 = 2x - 2

x = 1.5 > 0

This case is not possible.

Option C: G(x) = 2x + 3

If x > 0 or x = 0

2x + 4 = 2x + 3

This case is not possible.

If x < 0

-2x + 4 = 2x + 3

x = 0.25 > 0

This case is not possible.

Option D: G(x) = 3x - 2

If x > 0 or x = 0

2x + 4 = 3x - 2

x = 6

This case is possible.

Therefore, the answer is option D.