If you don't put your garbage in the designated garbage bags, they won't collect it.
If you don't put your garbage in the right bags, they won't take it away.
この場合、次のような言い方ができます。
ーIf you don't put your garbage in the designated garbage bags, they won't collect it.
「ゴミを指定のゴミ袋に入れないと、収集してくれないよ」
the designated garbage bags「指定のゴミ袋」
to collect「収集する」
ーIf you don't put your garbage in the right bags, they won't take it away.
「正しいゴミ袋にゴミを入れないと、持って行ってくれないよ」
the right bags「正しい・適切な」
to take away「持って行く」
ご参考まで!