smc

We will simulate the process in steps. In the beginning, we have: $4$ ounces of coffee in cup $1$ $4$ ounces of cream in cup $2$ In the first step we pour $4/2=2$ ounces of coffee from cup $1$ to cup $2$, getting: $2$ ounces of coffee in cup $1$ $2$ ounces of coffee and $4$ ounces of cream in cup $2$ In the second step we pour $2/2=1$ ounce of coffee and $4/2=2$ ounces of cream from cup $2$ to cup $1$, getting: $2+1=3$ ounces of coffee and $0+2=2$ ounces of cream in cup $1$ the rest in cup $2$ Hence at the end we have $3+2=5$ ounces of liquid in cup $1$, and out of these $2$ ounces is cream. Thus the answer is $\boxed{\frac{2}{5}}$.