Question 31037
Simplify:
{{{(2x^2+x-6)/(2x+4)}}} Factor the numerator and the denominator, as you have done.
{{{((2x-3)(x+2))/2(x+2)}}} Cancel the common factors (x+2)
{{{(2x-3)/2}}} Which is the answer that you got!

The restrictions that you have placed on the variable x don't seem to be correct.
If you look at the original expression, you will see that only when x = -2 will the denominator become zero.  So the restriction on x ought to be x cannot = -2.

Does this make sense?