The first person had 1/4 of all his teeth removed, a total of 1/4*32 = <<1/4*32=8>>8 teeth.
The second person had 3/8 of his teeth removed, meaning 3/8*32 = <<3/8*32=12>>12 of his teeth were removed.
Together, the first and the second person had 12+8 = <<12+8=20>>20 teeth removed in total.
The third person had half of his teeth removed, which were 1/2*32 = <<32/2=16>>16 teeth.
The first three people had a total of 20+16 = <<20+16=36>>36 teeth removed from their mouth.
The last person only had 4 teeth removed, bringing the total number of teeth removed at the dentist clinic to be 36+4 = <<36+4=40>>40 teeth.
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