A problem of spoken Japanese

たのしんで is the "て type" of the verb しむ (たのしむ).

At first, it was a continuum of しむ +しみ, and it became しんで after the sound change.

Please enjoy, look forward to, be happy, etc.

There is no context here, and it is impossible to determine the meaning clearly.

I didn't change it from しぃ ~