For an object to be in equilibrium, resultant of all moments(Principal of moments) must be equal (I.e anti clockwise moments= clockwise moments) & Resultant of all forces (Fres)=0 as well.
AB is the whole length of the rigid rod which is 2.8
Imagine point A at one end and a force acting on it downwards 20N (There is also a contact/reactant/normal force acting on it on the opposing direction so that sets the Fres=0) "If the rod is pivoted at 1.2m from end A" Well the whole length of the rigid rod is 2.8, away from A 1.2m where is the pivot so the pivot away from point B would be 2.8-1.2=1.6m
Now let the pivot be y
let force that acts on A be z
let force that acts on B be x
so
Ay*z must be equal to By*x
we know the distance Ay and By also we know z but we want to find x so that Ay*z=By*x
so subsituite,
Ay=1.2m
z=20N
By=1.6m
1.2*20=1.6*x
24=1.6*x
x=24/1.6=15N
The force that acts on B so that the rigid rod is in equilibrium is 15N