Quantization step-size for a given signal based on its PDF
You have a uniform input PDF, and the optimal quantizer for a uniform inpu will be a uniform quantizer. Note that the your uniform PDF has two pieces and the interval from $-4$ to $4$ is completely untreated. 

Then, assuming a 2-bit (4 level) uniform midrise quantizer with the given PDF your decision intervals $I_k$ and reconstruction levels $y_k$ will be as follows:

$$ x \in I_1 = [-6,-5] \implies y_1 = -5.5 $$
$$ x \in I_2 = [-5,-4] \implies y_2 = -4.5 $$
$$ x \in I_3 = [4,5] \implies y_3 = 4.5 $$
$$ x \in I_4 = [5,6] \implies y_4 = 5.5 $$