She pushed the door open.

Literal

She [topic-は] door [object-を] push-opened.

押し開ける is a compound verb fusing 押す (push) with 開ける (open) — Japanese builds many such verbs by stacking the manner of an action onto its result, giving you motion and outcome in one word. Compare 押し込む (push-into), 押し付ける (push-onto). 戸 is a generic word covering all kinds of doors — sliding, hinged, even gates — so the imagery isn't necessarily a Western swing-door.