I'll help you.
This skit is from the 1969-1970 first season and can be found on the episode where Big Bird tries to move his birdseed from Hooper's Store back to his nest.
You're right about the live action skit where you see a hand filling an egg carton with eggs one-by-one and a child's voice counts each one until...
...another person's hand drops a vanilla oreo cookie into the 10th slot, and the voice goes: "nine eggs and one cookie.....ten eggs and one cookie....eleven eggs and one cookie"
....the kid then takes the cookie out of the slot, eats it, and replaces it with another egg and says: "twelve eggs and no cookies.
I think this skit was designed to teach ADDITION AND SUBTRACTION.
Then Ernie (in his groovy psychedelic 1969 shirt) does the same thing, except reverses the eggs with 11 cookies and 1 egg. Cookie Monster, or should I say "Monster" as he was called back in 1969, pops up and eats all the cookies (showing SUBTRACTION) and then, for the grand finale,
throws the 1 egg into his mouth and walks off, leaving Ernie sobbing like a baby.