The total amount spent both on tickets and snacks was $34. 4 sets of $6 tickets = $24. That leaves you with $10 left to be spent. 4 divided by 10 is 2.5. So each bag cost $2.50.
Kara incorrectly factored 2(16x^2 + 24x + 9) she did not find the correct factors when she factored out. The correct factored expression would be 2(4x+3)^2