Question

how is the local time of a place fixed

Answer 1

Local time of place is fixed with reference to the apparent movement of the sun.


For example:

where the sun is over head in the sky I is mid day or 12 noon...

Answer 2

The local time of a place is fixed according the movement of Sun in Sky based on which local time is calculated.  

Explanation:

This time is differing from the standard time. Earth is rotating on its axis and get the sunlight in the various parts of the earth. Sometimes some part of the earth gets light then there day is happened and in the other side there no sunlight is present so there night is happened.

So various places of the earth receive sunlight in various times of the day. So the local time should be different in different place. But the local time of any one place is fixed.