The scale is balanced. This is the case if the distances * weights are the same on both sides of the scale: (A + B) * weigth 1 + B * weight 2 = C * weigth 3 + (C + D) * weight 4.
(200 + ?) * 2 + ? * 4 = 100 * 8 + (100 + 120) * 2.
==> (200 + ?) * 2 + ? * 4 = 1240.
==> Write without parentheses: 200 * 2 + ? * 2 + ? * 4 = 1240.
==> Simplify: ? * 6 + 400 = 1240.
==> ? * 6 = 1240 - 400.
==> ? = 840 / 6.
==> ? = 140