When balancing a meter stick, the torques have to be equal, but the forces to not.
To find torque, you must know the equation
Torque= Force * Lever Arm
The meter stick was balanced in a way similar to the following picture
Since it was balanced, we knew the clockwise and counterclockwise torques were equal.
So, we multiplied the force and lever arm of the weighted side to find the torque.
Then, we divided that number by the length of the opposite lever arm.
This gave us the force of that side of the meter stick.
When you divide this number by the numerical value of gravity, you will have the mass!
