Essentially, use the Sum of the Turning Moments = 0 for static equilibrium. Choose the obvious turning point, which is "B". Also note that when the beam starts to lift, the reaction at support A will be zero.

First Step. Identify the forces. 20 metres of u.d.l. on the l.h.s. of the fulcrum, 4 metres of u.d.l. and the point load X on the r.h.s. Using Newton's Principle of Centre of Effort, replace 20 metres x 2 kN/m = 40 kN with a point load of 40 kN located at 10 metres to the left of B (why at 10 metres to the left of B? think about it!) Replace the 4 metres x 2kN/m with a point load of 8kN located 2 metres to the right of point B.

Second Step. Sum the turning moments about B. (- 40 kN x 10 m) + (8kN x 2m) + (X x 4m) = 0 and solve for X.

Notice that I have adopted the sign convention that anticlockwise turning moments are negative, and clockwise turning moments are positive.