Tasha has 12 bills in her wallet. She has a total of $82. If she has twice as many $5 bills as $1 bills and two more $10 bills than $5 bills, how many of each does she have?

Let x be the number of $1 bills.

Tasha has 2*x $5 bills
Tasha has 2*x+2 $10 bills.
The total number of bills is x + 2*x + 2*x+2 = 12.
Combining like terms, we get 5*x+2 = 12
Subtracting 2 from both sides, we get 5*x = 10
Dividing both sides by 5, we get x = 2.
Tasha has 2 $1 bills, 2*2 = <<2*2=4>>4 $5 bills, and 4+2 = <<4+2=6>>6 $10 bills. Answer: \boxed{2, 4, 6}.