Step 1 :To find the y-intercept, we set x = 0 in the function: \(f(0)=2 \log _{4}(2-0)-2 = 2 \log _{4}(2)-2 = 2*0.5 - 2 = 1 - 2 = -1\). So, the y-intercept is \(\boxed{(0, -1)}\).
Step 2 :To find the x-intercept, we set f(x) = 0 in the function: \(0=2 \log _{4}(2-x)-2\). Solving this equation gives us: \(2 = 2 \log _{4}(2-x)\). Dividing both sides by 2 gives us: \(1 = \log _{4}(2-x)\). Using the property of logarithms, we can rewrite this as: \(4^1 = 2 - x\). Solving for x gives us: \(x = 2 - 4 = -2\). So, the x-intercept is \(\boxed{(-2, 0)}\).
Step 3 :The domain of a logarithmic function is the set of all real numbers for which the function is defined. In this case, the function is defined for all x such that 2 - x > 0. Solving this inequality gives us x < 2. So, the domain is \(\boxed{(-\infty, 2)}\).
Step 4 :The vertical asymptote of a logarithmic function is the vertical line x = a, where a is the value that makes the argument of the logarithm equal to zero. In this case, the argument of the logarithm is 2 - x, so the vertical asymptote is the line \(\boxed{x = 2}\).