HMMT 2012 S5

Steph and Jeff each start with the number 4, and Travis is flipping a coin. Every time he flips a heads, Steph replaces her number $x$ with $2 x-1$, and Jeff replaces his number $y$ with $y+8$. Every time he flips a tails, Steph replaces her number $x$ with $\frac{x+1}{2}$, and Jeff replaces his number $y$ with $y-3$. After some (positive) number of coin flips, Steph and Jeff miraculously end up with the same number below 2012. How many times was the coin flipped?