энүүнтэй = энэнтэй = энэтэй
The base word is "энэ", in Japanese it would be "こいつ". This word is used a lot together with its other form - энүүнгүй /энэнгүй/ энэгүй. For example:
Энүүнтэй энүүнгүй миний ажил бүтнэ.
My work will be a success with or without his / her help.
Энэнтэй энэнгүй амьдарч чадна.
I can live with or without him / her.
Энэтэй энэгүй би болгочихно.
I can do it with or without him / her / it.