How much Ibuprofen can you take?

Lots of it.

According to Wikipedia, you can have at once up to 100 mg/kg in your body without toxic effects. That's about 40 tablets of 200 mg if you're 160 pounds. Of course, that varies also with age, healthy, and individual sensitivity, so better not to try those 40.

That's for a single big event. If you take it regularly, probably there is some reason for the indication to be taking a 400 mg (or 800 mg?) tablet every 6h.