He has 6 - 2 = <<6-2=4>>4 cats.
He has 4 - 1 = <<4-1=3>>3 parrots.
He has 4 + 6 = <<4+6=10>>10 snakes.
He has a total of 2 + 4 + 3 + 10 = <<2+4+3+10=19>>19 pets.
#### 19