私への感謝の気持ちは、晩御飯で示してね。
= Watashi eno kansha no kimochi wa bangohan de shimeshite ne.
= Try expressing your appreciation for me by (buying me) dinner.
How to use の ( = no) : one ( indefinite pronoun)
「どのおもちゃで遊ぶ？」
= Dono omocha de asobu?
= Which toy do you want to play with?
「ブタのか、お寿司ので遊ぶ！」
= Butano ka osushi no de asobu
=I will play either with the pig one or the sushi one!