I have to do an inventory count at the store where I work after it closes at the end of the month, so I can't make it to my English conversation class.
この場合、次のような言い方ができますよ。
ーI have to do an inventory count at the store where I work after it closes at the end of the month, so I can't make it to my English conversation class.
「月末に閉店後、働いている店で棚卸しをしなければいけないので、英会話クラスに行けない」
to do an inventory count「棚卸しをする」
can't make it to「…に行けない」
ご参考まで!