Step 1: Oxygen types in P$_4$O$_8$.
There are terminal P to O oxygens and bridging P to O to P oxygens.
Step 2: Split the eight oxygens.
Four oxygens are terminal, one on each phosphorus, leaving four bridging oxygens.
Step 3: Count the bridges.
Each bridging oxygen makes one P to O to P bridge, so there are four bridges.
Step 4: Answer.
\[ \boxed{4} \]