How would you find the mass of a block sitting on a table using forces if there is a block hanging off the table of 10 kg and the tension in the line connecting the two blocks is 12 N? (ignoring surface friction for the block on the table)

If you know the acceleration of the system which has been set up, you simply use the F = ma equation.

m being the total mass of the system, that is the 10 kg + mass of block you're looking for.

F is what is pulling the 1 kg block downwards and a is the acceleration of the system.