Can I connect two taps of a tapped transformer together to make a center tapped transformer?
No. That connection creates a short circuit on the secondary.
If you're lucky, it will draw enough current to blow your primary fuse. If you're unlucky, it won't blow the fuse, and will overheat the transformer.
You already have the solution with that transformer. Use the 8 V tap as the centre tap between 0 and 16 V, and ignore the 24 V tap.