Can This Elevator Ever Reach Floor Seven?

Can this elevator ever reach floor seven from the ground floor? THE RULES Start at floor 0. Buttons move up exactly 4 floors or down exactly 6. The tower has floors 0 to 20; moves outside it are disabled. You have 12 seconds before the explanation. Pause if you want more thinking time. Did you solve it before the last tick? Share your answer and reasoning in the comments. Subscribe to Last Tick Logic for more puzzle challenges. #LogicPuzzle #MathPuzzle #BrainTeaser