The e^-6s part means that this part of your signal is delayed in time by 6 seconds. so you can do the inverse transform without it and then when you get your time signal for this part, delay it by 6 seconds. So replace t with t-6 in your answer for the time equation and you should be good.
help on state space HW
Edited by HallsofIvy
I have removed this because
1) It introduced a totally new problem, not that of the original poster.
2) It has also been posted under "homework".