Actually I figured out that I had to include the tension on both sides.
For the left side: F-T=ma therefore F=T. The on the right side, mg-2T=ma. Therefore mg/2=F. I got the correct answer as 293N.
However, there is a second part that I don't understand.
The canister is lifted 5.4 cm. During that lift, what is the work done on the canister by the weight mg of the canister? (Hint: When a cord loops around a pulley as shown, it pulls on the pulley with a net force that is twice the tension in the cord.)
I know that W=F*d. I tried setting W=2F*d, but that's not right.