Question 666521
To find the expected value of the game, you take all possible outcomes, multiply each by the probability of that outcome, and add them all up.  
  
For this game, we have three possible outcomes:  $2, $8, and $12.  From your description of the game, the $2 space occupies half the spinner, and the $8 and $12 outcomes each occupy one fourth of the spinner.  Assuming the pointer is completely fair, the probabilites are:
p($2) = 0.50
p($8) = 0.25
p($12) = 0.25
  
Multiplying each outcome by its probability, we get:
$2.00 * 0.50 = $1.00
$8.00 * 0.25 = $2.00
$12.00 * 0.25 = $3.00
  
Adding all these up gives us an expected outcome of $6.00 against the $8.00 cost to play the game.
  
Over time, a person playing the game should expect to lose an average of $2.00 per play.
 
You didn't define "fair" but I'm going to assume that it means that a player should expect to break even on average.  With that definition, a fair price to play the game would be $6.00 per turn.