when was the last season aired?
9 June 1968
Round the Horne
The fourth series began on 25 February 1968 and ran for 16 episodes to 9 June. 
what is round the horne? A BBC Radio comedy program who is the director of the program? UNANSWERABLE
wiki:5386091
Round the Horne [SEP] 1967–1968: Series 3 and 4
The cost fell from £601 a show in series 3 to £486 in series 4. That year's Christmas special was broadcast with the new line-up and writers. The fourth series began on 25 February 1968 and ran for 16 episodes to 9 June. After the first episode Williams was unimpressed with the new material, and wrote in his diary "Now there are 4 writers on it! It is unbelievable really. Four! For half an hour of old crap with not a memorable line anywhere ... of course one goes on and flogs it gutless and the rubbish gets by". Without Feldman, Took was enjoying the show less than he had previously.