The speaker plans to find a new job within six months or less.

"See" means "imagine" or "expect". "Myself" is the direct object: "I don't see myself". The rest of the sentence "being..." is an adjective clause that modifies "myself". Grammatically, the sentence is similar to "I don't see myself employed for longer than another six months".

He is goin to quit the job in the next sux month.