(a^2-8a+16)/(b^2-9)*(2b-6)/(a-4)

To simplify the expression \(\frac{{a^2-8a+16}}{{b^2-9}} \times \frac{{2b-6}}{{a-4}}\), we can factorize the quadratic expressions in the numerator and denominator and simplify the fractions where possible.

Firstly, factorize the quadratic expressions: \(a^2-8a+16 = (a-4)(a-4)\) and \(b^2-9 = (b-3)(b+3)\).

Now, we rewrite the expression: \(\frac{{(a-4)(a-4)}}{{(b-3)(b+3)}} \times \frac{{2b-6}}{{a-4}}\).

Simplify by canceling out common terms: \(\frac{{2(a-4)}}{{b-3}}\).

Therefore, the simplified expression is: \(\frac{{2(a-4)}}{{b-3}}\).