〜目
The …th (ordinal numbers)machine translation
FormationNumber + counter + 目 (一つ目・二人目・三回目・四年目)
Attach 目 (read め) after a number + counter and you turn a "quantity" into an "ordinal": 二つ (two things) → 二つ目 (the second one), 三回 (three times) → 三回目 (the third time), 二人目 (the second person), 四年目 (the fourth year), 三日目 (the third day). Every counter you've learned works with 目.
This pattern is especially handy when giving directions — count the turns with 〜つ目: 二つ目の角を右に曲がってください (turn right at the second corner). Note that when modifying a noun you need の: 三番目の人 (the third person).
Don't confuse 〜回目 with 〜回 without 目: 三回 means "three times (in total)", while 三回目 is "the third time". 日本へ三回来ました (I've come to Japan three times) is different from 今回は三回目です (this is my third time). For frequency like 週に三回 (three times a week), see the lesson on the particle に for frequency.
Examples
二つ目の角を右に曲がってください。
Please turn right at the second corner.
日本へ来るのは三回目です。
This is my third time coming to Japan.
日本に住んで、今年で四年目です。
As of this year, it's my fourth year living in Japan.