The question is:-
The graph of $y = f(x)$ is given below. How many zeroes are there of $f(x)$?
The answer is given One.
But as far as I know, if the graph of a function crosses the x-axis, it indicates a zero with an odd number of multiplicity, so the number of zeros can be any odd natural number.
How we can say that the number of zeros is exactly one?
Please help.
I think you're confusing the term "number".
The question is asking for how many zeroes (roots) there are, not the number of multiplicity. All this requires you to do is count how many times $f(x)=0$.
It looks in the picture like there is one such zero (at the origin), so that is why the answer given is one. Compare that to this picture:
In that picture, there are three zeroes.