i'll use x instead of r and h.
i will also re-sort the terms so that the higher order term is to the left of the lower order term.
your equation becomes:
(4x^3 + 4x^2 - 7x - 6) divided by (2x + 3).
in order to perform synthetic division, the divisor has to be a first order expression and the coefficient of the leading varikable has to be 1.
you accomplish this by dividing both numerator and denominator by 2.
you equation becomes:
(2x^3 + 2x^2 - (7/2)x - 3) / (x + (3/2))
you can now perform the synthetic division as shown below:
the normal division gets you the same answer as shown below:
if you need a tutorial on how to do normal division and how to do synthetic division, these are good sources:
http://www.purplemath.com/modules/polydiv2.htm
http://www.purplemath.com/modules/synthdiv.htm