Burmester-Desmedt (BD) key agreement protocols
All this work is done modulo the prime $p$ (which is 11 in your toy example); in this field, addition, subtraction and multiplication is done in the usual way (except you do a modulo $p$ at the end); however division is defined differently.

We define $x = 6/4\  (\bmod 11)$ to be that value such that $x \times 4 = 6\  (\bmod 11)$.

Now, we see that $7 \times 4 = 28$ and $28 = 6\  (\bmod 11)$, hence $6/4 = 7$.  And, yes, if $p$ is prime, and if what you're dividing by is not zero, then it turns out that such division is uniquely defined; there will always be precisely one number between 0 and $p-1$ that meets this criteria.

How do we find such values $x$.  Well, when $p$ is small, you can just test the various possibilities (like I did in this case).  However, if $p$ is large, you can efficiently find such values using the Extended Euclidean Algorithm