Answer: one point only.
Step-by-step explanation:
Since the length of the sides of the square is 9 cm, taking a point outside the square which is equidistant from point B and C will never give exact 6 cm from A.
The only way to achieve this is by taking a equidistant point inside.
You can achieve exactly 6 cm from point A from point between B and C
But can only achieve a single point if it has to be equidistant from point B and C.