To find (b-c)^6, we can first rewrite (b-c) as a variable, let's say, x.

So x = b - c

Then, we can rewrite the given equation in terms of x:

x^2 - 2bc + c^2 = 9

Now, we can substitute x back in terms of b and c:

x^2 = (b - c)^2
= b^2 - 2bc + c^2

Therefore, x^2 = b^2 - 2bc + c^2

So, our equation becomes:

x^2 = 9

Now, to find (b-c)^6, we need to raise x to the power of 6:

x^6 = 9^3
= 729

Therefore, (b-c)^6 = 729.