Answer
$V_B-V_A = -32.0~V$
Work Step by Step
We can use Equation (24-18) to find the potential difference:
$V_B-V_A = -\int_{A}^{B}~E~dx$
$V_B-V_A = -\int_{0}^{4.00}~(4.00~N/C)~x~dx$
$V_B-V_A = -\frac{(4.00~N/C)~x^2}{2}~\Big\vert_{0}^{4.00}$
$V_B-V_A = -[\frac{(4.00~N/C)~(4.00)^2}{2} - \frac{(4.00~N/C)~(0)^2}{2}]$
$V_B-V_A = -32.0~V$