Has a hand in the matter
His hand is involved in the matter. Someone was involved in what happened.
("And any foreign hand involved in the matter is exempt from the firstborn" - Bava Metzia 70b)
Translation
Expression (Hebrew)
יָדוֹ שֶׁל...בָּאֶמְצַע
Definition (Hebrew)
יָדוֹ שֶׁל...מְעֹורֶבֶת בַּדָּבָר. פְּלוֹנִי הָיָה מְעֹורָב בַּנַּעֲשֶׂה.
("וְכָל יָד נָוכְרִית בָּאֶמְצַע פָּטוּר מִן הַבְּכוֹרָה"-בָּבָא מְצִיעָא ע ע"ב)