See https://www.circuitlab.com/circuit/gej8eb/screenshot/540x405/

Given
iA(t) = [0.6 * e ^ (-2t)] A
iB(t) = [1.2 * e ^ (-2t) - 0.4] A
i(t) = [1.8 * e ^ (-2t) - 0.4] A

find = my solution
v1(t) = -7.2 e ^ (-2t)
v2(t) = -28.8 e ^ (-2t)
v(t) = -36 e ^ (-2t)

book
v1(t) = -36 e ^ (-2t)
v2(t) = -7.2 e ^ (-2t)
v(t) = -28.8 e ^ (-2t)
reality check: KVL violated: v(t) != v1(t) + v2(t)

am I misunderstanding something, or is the book solution misprinted?

 

Yes, your answer is correct.
Just use the formula:

\(V_{L}(t) = L \frac{di(t)}{dt} \)