Synthetic division is easiest. Change x+2 into -2 as a zero of the polynomial, then divide:
-2 | 4 13 12 4 (coefficients in descending degree order)
+ 4 -8 -10 | -4 (copy leading coefficient; multiply result of previous column by -2)
(Add the two rows)
4 5 2 | 0 remainder. The vertical bar separates the quotient from the remainder.
Insert the powers of x: 4x2+5x+2 is the quotient.