Heterogeneous Range Hoeffding Bound

Independent centered shocks satisfy \[ X_1\in[-1,1],\quad X_2\in[-2,2],\quad X_3\in[-3,3],\quad X_4\in[-4,4] \] almost surely. Use Hoeffding's inequality to bound $P(X_1+X_2+X_3+X_4\ge 6)$.