You simply walk in, put purchases into a basket and walk out the door without so much as to make eye contact with anyone.

英訳に間違いが有れば正してください。

ただ店に入り買った物をかごに入れて誰とも視線すら交わさず店を出ます。
You simply walk in, put purchases into a basket and walk out the door without so much as to make eye contact with anyone.

ヒント
without

答え to makeをmakingにする

You simply walk in, put purchases into a basket and walk out the door without so much as making eye contact with anyone.

withoutの間にso much asが挟まった文でmakingはwithoutの目的語

without so much as doing
…すらしないで