Plug Walk I

The plug performs a random walk on the set $S = {0,1,\dots, m}$ , where $m > 0$ . The plug starts at position $0 \leq k < m$ . Each step, the plug moves up or down $1$ step with equal probability. The plug has opps at $0$ , so they move back upwards with probability $1$ whenever they hit $0$ . Find the expected amount of steps that occurs until the plug first reaches position $m$ when $k = 4$ and $m = 20$ .

Answer format: enter an integer.