The problem requires I determine the value of I0, I think my solution is correct but I don't know how to check because I got the problem from a text with no answers. Looking for more experienced eyes to check for me.
As far as I can tell the solution is correct. I got \$v_1 = -32V\$, \$v_2 = 24V\$, \$v_3 = -32V\$, \$I_0 = -4A\$. If you are ever unsure, try using a simulator. It's a great way to verify your solution.
For example, the schematic below can simulate your circuit. And it outputs -4A as well.
I've known some very smart people who would first look at the assignment with some glaring eyes and observe:
"4*8 = 8*4 = 32..., what if all the 4A went through branch 0-v1, then 2Io=8A would flow through branch 0-v3 because both v1 and v3 would be 32V hence i3 will then be 0 anyway (and v2=2*12=24V). Check!"
It always amazed me how they did it and somehow I think this question was looking for people like that.
But anyway, your answer is correct. :)