Step 1: Beta oxidation is the default route for breaking down straight chain fatty acids, cutting off two carbon acetyl units in each cycle by oxidizing the beta carbon.
Phytanic acid carries a methyl group right at the third carbon, the same beta carbon that beta oxidation enzymes need to act on, so the branch physically blocks the usual reaction from starting.
The cell's workaround is alpha oxidation, which shortens the chain by one carbon at the alpha position first, shifting the branch away from beta position so that beta oxidation can then continue normally. Answer: alpha oxidation.