The co-finite topology on a finite set $X = \{s,t,u\}$ (with $|X|=3$) consists of all subsets whose complements are finite — but since $X$ is already finite, this means $\tau$ contains $\emptyset$ and all subsets whose complement is finite, which is all subsets. So $\tau$ is the discrete topology: $|\tau| = 2^3 = 8$.