Circuit analysis with node voltage method
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.







simulate this circuit &ndash; Schematic created using CircuitLab