In a ΔABC, If 2∠A = 3∠B = 6∠C, then the value of ∠B is:

According to question,
Given :
$$\eqalign{ & 2\angle A = 3\angle B \cr & \frac{{\angle A}}{{\angle B}} = \frac{3}{2}\,\,\,\,\,\,\,\,\,\,\,\,\,3\angle B = 6\angle C \cr & \frac{{\angle B}}{{\angle C}} = \frac{6}{3} = \frac{2}{1} \cr} $$
To make angle ∠B same
∴ ∠A     :     ∠B     :     ∠C
      3     :        2     :     1
As we know that
∠A + ∠B + ∠C = 180°
3x + 2x + x = 180°
x = 30°
∠B = 2x
∠B = 60°