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I am not so sure about the puppets, but the crafty hands mentioned by Meek Cria sounds an awful lot like Zzzap! - try searching "zzzap hands" on youtube or something if still looking.
Edited by thecatcalledfishYes! Zzzap was definitely the one with the hands, thank you thecatcalledfish, I must have mixed in the two shows. I still remember the one you're referring to Will Keaton!

Not much to go on with this one. All I recall is a puppet based show that took place in front of or behind this big wood counter. I recall it being based at teaching kids stuff, like one time they explained that gravity made stuff fall down, and demonstrated this by throwing a ball off the top of the screen, only for the ball to NOT fall back down into view. It would have been on the air in the late 80's or early 90's and I'm reasonably confident it came on right before Cheers, because I remember watching the opening to Cheers, thinking it might be a second episode of this show, only to be disappointed.