If 8 paper clips are placed on one side of the balance 2 cm from the fulcrum,where should 4 paper clips be placed on the other side?

Four cm away, so that the product of (number of clips) x (distance from fulcrum)

is the same on both sides

8x2 = 4x4

What you are requiring is that the moments are in balance, so that the net torque about the fulcrum is zero.