**Hint**: In the given question, we have been asked if a ray can be extended to any of the two sides as much as wanted. To answer this, we must know the definition of what ray is, compare it with the given statement and correct it if needed.

__Complete step-by-step answer__:

A ray is a geometrical figure which resembles a line except for one thing, that it is fixed on one side. A line is the figure which can be extended to any side.

Now, the given statement is: “A ray can be extended indefinitely on either side.”

Hence, this statement is false.

So, the correct statement is

A line can be extended indefinitely on either side.

or, A ray can be extended indefinitely on one side.

**Note**: So, for solving questions of such type, we first write what has been given to us. Then we write down what we have to find. Then we think about the concept or formula which contains the known and the unknown and pick the one which is the most suitable and the most effective for finding the answer of the given question. Then we use the results or finding of the concept and apply it to our question. It is really important to know and follow all the results of the concepts if we have to solve the question correctly, as one slightest error gives the incorrect result.