Calculate rate of drainage.
Tap 1 1P/ 4min or 1P/4min x 1g/8p = 1g/32min

Tap 2 1q/6min or 1q/6min x 1g/4q = 1g/24min

So we know every 32 mins, 2 gals leave the barrel. We just have to figure out how many 32 mins are there in 492 mins . (the number of mins from 12noon to 8:12pm)

For example
(24 mins after Noon)
12:24 1 gallon is drained
( 8 mins later)
12: 32 1 gallon is drained ( 32 mins elapsed)
( 16 mins later)
12: 48 1 g
( 16 mins later)
1:04 1 g ( Another 32 min elapsed)

( 8 mins later)
1: 12 1g
(24 mins later)
1: 36 1g ( The thrid 32 mins have elapsed) And the pattern is repeated.

It would be painful to continue this so we multiply the rate 2g/ 32min by 492 mins to see how many gals have drained by 8: 12PM.
2g/32 x 492 mins = 30 12/16 g or 30 3/4 g

36 - 30 3/4 = 6 3/4 g which is not among the answer choices.

You could also set up from the pattern that
6/96 = X/492 ( if 6 gallons are drained in 96 mins, how many will go in 492 mins)

Which gives the same 30 3/4

36 gallons of beer=36*8 pints=288 pints
Total time of drainage=8 h 12 min=492 minutes
First tap will drain 492/4=123 pints in 492 minutes.
Second tap will drain 492/6=82 quarts=164 pints in 492 minutes.
Total withdrawal=123+164=287 pints
Remaining beer=288-287=1 pint
Option B