An object has moved through a distance. Can it have zero displacement? If yes, support your answer with an example?

First of all, One needs to understand the fundamental difference between Displacement and Distance; Displacement is vector Qty which has Magnitude as well as direction (For ex: I travelled 100m in north direction ) whereas distance has the only Magnitude ( For ex: I went 50 km ). Therefore Displacement could be zero if the Initial point and endpoint are the same but covered a certain distance. Ex: If a man starts running in a stadium having a circular track and reach back to its Initial point after 1 round, Then the Total distance covered here is Circumference of circular path whereas the Displacement is Zero as the initial point and endpoint are same.

Travel from your house which is at B (point to be noted that, B is your starting point) then you go to TreeTree at position C, and from C to tree A, and then back to your house and you stop, So your ending point is also B (your home).
Now , the distance travel by you is = 3m+5m+4m = 12m
which you get it,
but as per the Displacement definition, it's always the distance/measurement between starting(initial) point to
ending final point, so your initial and starting point, the Displacement is zero
but if you stop at TreeTree on point A, then your starting point was at B and ending point at A
So the measurement between them is 4m So your Displacement at that case is 4.
I understood it, then what will be the distance if you stop at Tree A?

Yes, the displacement can be zero. Suppose a person is walking on a rectangular park ABCD, he starts with A moves to B then to C and finally reaches to A, here starting point & final point coincides, hence displacement = 0, although the person has travelled a distance which equals to its perimeter.