Joe S. answered 09/11/14
Advanced degrees in Business, Finance, and Statistics
You can simplify things a bit by finding R6, the equivalent resistance of R1 and R2 in parallel = 2*6/8 = 1.5.
Call i6 the current thru R6 (in the same direction as i2).
Looking at the node for currents i6, i4, and i3, they must sum to 0, so i3+i4+i6=0
we know i4 = -11 from the current source, so i3+i6 = 11
The voltages across the resistors must sum to the voltage source of 6V
v3 = i3*R3
6*i3 -1.5*i6 = 6
Solving gives i3 = 3, i6 = 8
v3 = +18V
v6 = -12 V
sum is +6V as required.
You can then find the currents in R1 and R2 using 12V across each one, which add to i6