Sorry for edit, accidentally posted.
Circuit is show in my attachment. I have 3 loops with three unknown currents.
8 Ohms of resistance down the left side.
6 Ohms of resistance and a 4V battery down the center.
4 Ohms of resistance and a 12V battery down the right side.
I honestly have no idea if I'm even approaching this correctly.
The Attempt at a Solution
Loop A (Big Loop)
-8I1 +12V +4I1 +4I3 = 0
-4I1 +4I3 = -12V
Loop B (Left)
-8I1 +4V -6I1 +6I2 = 0
-14I1 + 6I2 = -4V
Loop C (Right)
-6I3 - 6I2 - 4V + 12V - 4I3 = 0
-10I3 - 6I2 = -8V
combine in a matrix
I1 I2 I3 V
a -4 0 -4 -12
b -14 6 0 -4
c 0 -6 -10 8
I1 = 1.083
I2 = 1.861
I3 = -1.917
Im not entirely sure, but I think these are voltages for the loops, so from there I would set
V= IR for each of the loops to find the current, but this produces the wrong answer. This is the easiest circuit in my textbook, and I have been searching the web for problems which is only making matters worse I think.
Any help would be greatly appreciated.