をおぼえてるか

do you remember …?

→ を
phrase Uncommon #12,717
do you remember …? The を marks what is being remembered. The ending か makes it a question; this phrasing is casual.
JA: 舎監の名をおぼえてるか?
EN: Do you remember the dorm supervisor’s name?

リチャードロシアのホッケー選手について頼んだことをおぼえてるか?

Do you remember what I asked about Richard, the Russian hockey player?

— Брат 2 (2000)

見た目はクリスティ・ラブだあの番組をおぼえてるか?

She looks like Christie Love. Do you remember that show?

— レザボア・ドッグス (1992)

ロシア人は皆そこへ行くあのホッケー選手のグロモフをおぼえてるか?

All Russians go there. Do you remember that hockey player, Gromov?

— Брат 2 (2000)