A 13.8 kg box is sliding up with an applied force of 35N with an incline that makes an angle of 15 degrees with respect to the horizontal. The coefficient of kinetic friction between the box and the surface of incline is .18. The initial speed of the box at the bottom of the incline is 1.5 m/s. How far does the box travel along the incline before coming to a rest?

I know the answer is .66 m , but need the way to get it. Thank you!

First step is to determine the sum of forces acting on the box in the direction of the incline - you have friction, a component of the box's weight, and the pushing force. With that you can determine the boxes acceleration from F=ma. Then apply the usual equation of motion to determine distance given initial velocity and acceleration.