After____(finish) his homework ,the boy went on___(play)computer games.

finishing playing
after是介词,介词后面,动词加ing
go on doing
继续做某事

finishing;playing

having finished
to play

前面是要过去完成时的分词形势
后面是go on to do sth

finshing,介词后用ing形式,to play,继续做某事

finishing介宾（after是介词，要跟名词性的动词）

playing (go on doing sthg 固定搭配，表示继续做什么)

finishing
因为After是介词,介词后面的动词加ing