first in one direction, then in another (either back and forth or in random directions)
this way and that
(up and down some place,) now this way, now thatto and fro.
К Елизавете Павловне присоединилась в первом ряду Чернышевская и по тому, как мать изредка поворачивала то туда, то сюда голову, поправляя сзади причёску, Фёдор, витавший по залу, заключил, что ей малоинтересно общество соседки (Набоков 1). Elizaveta Pavlovna was joined in the first row by Mme. Chernyshevski, and from the fact that his mother occasionally turned her head this way and that while adjusting her hairdo from behind, Fyodor, hovering about the hall, concluded that she was little interested in the society of her neighbor (1a).
Там, возле наполовину растасканной на дрова летней читальни, была вытоптанная нашей школой площадка. Старшеклассники, разбившись на две ватаги, проносились по ней то туда, то сюда (Аксёнов 2). There, next to the summer reading room-which had been half torn down for firewood—our school had trampled out a playing field. The upperclassmen, who had sp lit up into two teams, raced up and down it, now this way, now that (2a).