4 twenty-pound dumbbells weigh 4*20 = <<4*20=80>>80 pounds.
When Parker added two more dumbbells to the setup, he increased the weight by 2*20 = <<2*20=40>>40 pounds.
The dumbbells that Parker used to do his exercise weigh a total of 40+80 = <<40+80=120>>120 pounds.
#### 120