$(15$ points$)$ For the given circuit,

a$)$ find the currents flowing through each resistor.

b$)$ What is the potential difference between points A and $B(V_A-V_B)?$

Answers: a$)4$ A through $R_4($downward$)$;

$6$ A through $R_3($upward$)$;

$2$ A through $R_2($downward$)$

b$)12$ V