Split the to-be-integrated interval into two:

$$\int_{0}^{2}\frac{dx}{\sqrt{|x-2|}}=\int_0^2\frac{dx}{\sqrt{2-x}}=-2\sqrt{2-x}|_0^2 = 2\sqrt{2}$$

$$\int_{2}^{4}\frac{dx}{\sqrt{|x-2|}}=\int_0^2\frac{dx}{\sqrt{x-2}}=-2\sqrt{x-2}|_2^4 = 2\sqrt{2}$$

Therefore, the final answer is $$2\sqrt{2}+2\sqrt{2}=\boxed{4\sqrt{2}}$$