Julie caught half the amount of Tabitha's 22 pieces so 22/2 = <<22/2=11>>11 pieces of candy caught by Julie
Carlos caught twice the amount of candy as Stan's 13 pieces so 2 * 13 = <<2*13=26>>26 pieces of candy caught by Carlos
All together, Tabitha caught 22 pieces, Stan had 13, Julie had 11 and Carlos had 26, so there were a total of 22+13+11+26 = <<22+13+11+26=72>>72 pieces of candy
#### 72