Bizarre Pea Stall

Simon is playing some carnival games, and one particularly odd stall requires him to toss a pea chip into a bottlecap. He is successful $40$% of the time, and misses the other $60$% of the time. His score starts at zero. Every time he manages to put the chip into the cap, his score goes up by one. Every time he misses, his score decreases by up to two, but it will never go negative.

What is the expected number of tosses that Simon will need to reach a score of $4$?

Submit your answer as an irreducible fraction, with the numerator and denominator separated by a slash. For example, if your answer is $0.8$, you should submit "4/5".

For all the tasks, including this one, you can submit as many times as you like with no penalty! Only your best submission will be counted.