He caught 12 more fish in the second round than he had caught earlier, a total of 12+8=<<12+8=20>>20 fish.
The total number of fish he caught in the two rounds is 20+8=<<20+8=28>>28
In the third round, Archer caught 60/100*20=<<60/100*20=12>>12 fish which were 60% more fish than the number he had caught in the second round.
This means he caught a total of 12+20 = <<12+20=32>>32 fish
Archer caught a total of 28+32=<<28+32=60>>60 fish on that day.
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