What is the original wording of the problem?
There is an isosceles triangle with a base of 12 units.
Find the locus of points that are 6 units from the midpoint on the line.
. . What line?
If it refers to the midpoint of the base, why mention the triangle at all?
We have a line segment 12 units long.
The locus of points 6 units from its midpoint is a circle:
. . center at the midpoint, radius 6 units.