First, rewrite the expression using this rule for exponents:
a = a^color(red)(1)
12/4(a^-2/a^-8)(b^-4/b^color(red)(1)) =>
3(a^-2/a^-8)(b^-4/b^color(red)(1))
Next, use this rule of exponents to simplify the a terms:
x^color(red)(a)/x^color(blue)(b) = x^(color(red)(a)-color(blue)(b))
3(a^color(red)(-2)/a^color(blue)(-8))(b^-4/b^1) =>
3a^(color(red)(-2)-color(blue)(-8))(b^-4/b^1) =>
3a^(color(red)(-2)+color(blue)(8))(b^-4/b^1) =>
3a^6(b^-4/b^1)
Now, use this rule of exponents to simplify the b term:
x^color(red)(a)/x^color(blue)(b) = 1/x^(color(blue)(b)-color(red)(a))
3a^6(b^color(red)(-4)/b^color(blue)(1)) =>
3a^6(1/b^(color(blue)(1)-color(red)(-4))) =>
3a^6(1/b^(color(blue)(1)+color(red)(4))) =>
3a^6(1/b^5) =>
(3a^6)/b^5