Jose took 500 mg of medication at 2:00 p.m., and then he took another 500 mg
at 6:00 p.m. However, 80% of the medication is cleared from his body every
2 hours. How many milligrams of medication remain in his body at 8:00 p.m.?
From 2:00 p.m. to 8:00 p.m., a total of 6 hours have passed (2 hours for each time interval: 2:00-4:00, 4:00-6:00, and 6:00-8:00).
During this time, the medication is cleared from his body four times (2 hours each time).
First, find how much medication remains in his body after the first 2-hour interval: 500 mg * 80% = <<500*80*.01=400>>400 mg
Then find how much remains after the second 2-hour interval: 400 mg * 80% = <<400*80*.01=320>>320 mg
Then find how much remains after the third 2-hour interval: 320 mg * 80% = <<320*80*.01=256>>256 mg
Finally, find how much remains after the fourth 2-hour interval: 256 mg * 80% = <<256*80*.01=204.8>>204.8 mg
Since we're only asked for the number of milligrams remaining, round down to 204 mg. Answer: \boxed{204}.