How many values of $x$ between $0$ and $100$, exclusive, satisfy both of the following conditions?
1. $x$ is a multiple of $4$.
2. $x$ is a multiple of $6$.
We can start by listing all the multiples of $4$ between $0$ and $100$ and then list all the multiples of $6$ between $0$ and $100.$ Then, we can find all the ones in common: $12, 24, 36, 48, 60, 72, 84,$ and $96.$ There are $\boxed{8}$ multiples. Notice that these are all multiples of $12$, which is the smallest common multiple we found of $4$ and $6.$