find all values of x

Multiply both sides by (x+2) * (x+4) or "cross multiply" to get:

$2x(x+4) = -6(x+2)$

Expanding out, we get:

$2x^2+8x = -6x - 12$

Adding 6x and 12 on both sides of the equation, we then get the quadratic:

$2x^2 +14x+12 = 0$

We can then factor this into:

$(2x+2)(x+6) = 0$

The values for which this is 0 are -1 and -6