To solve this equation, we first need to simplify the expression inside the logarithm:

x^6 - 6x^4 + 12x^2 - 8 = 0

Now we can rewrite the equation:

log0.5(x^6 - 6x^4 + 12x^2 - 8) = -3

Substitute the simplified expression:

log0.5(0) = -3

Since the logarithm of 0 is undefined, this equation has no solutions.

Therefore, the equation log0.5(x^6 - 6x^4 + 12x^2 - 8) = -3 has no real solutions.