。
She ran toward the door.
Literal
She [topic-は] door [genitive-の] direction [toward-へ] ran.
ドアの方 (doa no hō) is the standard 'in the direction of the door' phrasing — 方 (hō) softens a strict location into a directional vector, useful when 'toward' is more important than 'to.' Pairing 方 with へ doubles down on direction-of-motion. Compare ドアに走った ('ran to the door') which would emphasize arrival at the door rather than the trajectory; ドアの方へ走った leaves it open whether she got there.