"Hit for six" was a cricketing expression. As Turlough once needlessly explained to Tegan Jovanka, it indicated that a ball which had been hit over the boundary line without bouncing on the ground first. (COMIC: The Forgotten) Such balls won their batsmen six runs. Ishtar Hutchings nearly "hit for six" to conclude the 2010 match between the Doctor's Invitation Eleven and the Cheldon Bonniface Invitation Eleven, but Sanki caught it before it could sail over the boundary. (PROSE: Happy Endings)
At the Cranleigh Hall match on 11 June 1925 (TV: Black Orchid), the Fifth Doctor once believed that he had hit one for six, but it was caught by Ace who then vanished, because the ball was, in reality, a segment of the Key to Time. The Fifth Doctor's immediate reaction to the play was simply to wonder whether the umpire would rule him out. (COMIC: Time & Time Again)
Behind the scenes
The phrase has seeped into the wider British culture, in which it's usually used intransitively (e.g., from the ball's perspective, as in, "to be hit for six") to mean some devastating action which has been visited upon the subject of the sentence. For instance, if you say, "I was hit for six by her beauty", you mean that you were completely blown away by how beautiful she was.
It can also, less commonly, be used transitively, to indicate that the subject of the sentence did something extremely well. For instance, if someone asks you how you did on an exam, you might say, "I hit it for six," to indicate that you'd aced it. In this sense, it's close to the baseball expression, "hit a home run".