If a no ball is bowled in T20 cricket, a free hit follows. Does the "free hit" delivery count as one of the over?
In other words, would an over in which the sixth delivery is a no ball contain 8 deliveries: 5 legal, 1 no ball, 1 free hit and then 1 legal?
If a single no ball is bowled in an over, there will be 7 deliveries in the over, not 8. Free hit just means that the batsman cannot be out of that ball (except run out, handling the ball, hitting the ball twice, obstructing the field), it does not mean that delivery is not counted (unless, of course, that delivery too is a no ball or wide ball).
For example:
Delivery 1: Legal delivery ==> Count: 0.1
Delivery 2: No-ball ==> Count: 0.1
Delivery 3: Legal delivery ==> Count: 0.2
Short Answer:
Yes, Free hit counts as one of the legitimate balls of the over. 
Explanation :
Whenever during a cricket match if the Umpire declares a no-ball the next delivery is signalled as a free-hit. This is counted as a legitimate ball if its not a wide ball or a no-ball again.
In your scenario :
Five legal balls + a no ball + the free hit = 7 balls (6 legitimate and 1 no-ball).
