Q: Check engine light on - persistent misfire 2008 Honda fit

Hello - the P0304 indicates, as you state, a persistent misfire on cylinder 4. This could be due to a bad plug or coil on that cylinder, or a clogged or leaky fuel injector, causing the misfire. "Reading" the color of the spark plug"on this cylinder MAY provide some clue as to a fuel issue (black/brown soot means too much fuel - leaky injector; white may mean not enough fuel - clogged injector). If you need to replace coils, make sure you replace all of them, and you get the same supplier for all 4 (Denso or Hitachi) - the ignition systems on this one are a bit touchy for matching replacement parts. Replacement spark plugs are less sensitive to this. I would recommend an engine inspection by a mobile, professional mechanic, such as one from YourMechanic, who will come to your location, diagnose this problem, give you an accurate assessment of damage and cost estimate for repairs.