@Heavenlover22 Said
Yes, it's possible: Psyduck can know Psychic, but not by TM. It's by an Egg Move. To do this, it requires a Slowpoke/Slowbro/Espeon/Slowking and a Psyduck/Golduck.I picked a Slowbro (Lv 55, female, traded from Pokemon Blue) and a Psyduck (Lv 24, male, caught in Pokemon Gold). And I gave the Slowbro to the Day-Care Man, and the Psyduck to his wife. After the Egg I got from them hatched, it wasn't a Psyduck. It's a Lv 5 Slowpoke with moves like Tackle, CUrse, and even got Flash and Surf (the two moves his father had.) Am I doing something wrong? If you have any ideas and/or tips, feel free to comment and tell me below.
As for the Egg Chart of Psyduck, read this
Egg Chart on Psyduck .
First of all, the father is the one that contributes egg moves while breeding and the mother contributes the species. Hence why you got egg moves from psyduck on a slowpoke offspring. In order to get a psyduck offspring with psychic you would need a male slowpoke/slowbro/espeon/slowking that knows psychic to breed with a female psyduck/golduck.
Second of all, because of the above I think your best bet is to train a male slowpoke/slowbro/espeon/slowking and breed that with a female psyduck caught in the wild. Technically, espeon learns psychic 1 level earlier than slowpoke in gen 2 so you might want to consider that if you don't mind the day and happy evolution requirements.