Do you have a better copy of the image?
The directions of the arrows are almost indiscernible. The top arrow, for example, could also point towards the right.
Also in you manual drawing the bottom right resistor is 15 Ohm whereas in the copy it looks like 16 Ohm.
The way your reasoning goes is o.k. (apart from the direction and the sign of the current source, which I would have backwards due to the direction of the arrow in the current source, but that's a minor aside).
You can cross check your result by evaluating the two other loops (using the values you calculated from the top loop) and checking for consistency of the values you get.