My last post included a video which demonstrated how manual screen printing is done. The actual print in that video had a halftone element in it and used process printing to form the logo.
Process printing is when one uses the colours Cyan, Magenta, Yellow, Black and sometimes white ink to form the finished print. These colours (which are halftoned) are printed one after the other and the actual blending of these overprints creates the actual image/ colours required.
The print below used the white as a base. Then the yellow was printed. The magenta (pink) is added to form the red and orange sections in the print.