But it can provide ideas:

f(x+2)=f(2-x)=f(x-2)

Therefore, f(x) is a periodic function with a period of 4 over the domain.

Another reason is that f(x) has four real roots in (-2,6), which is equivalent to having two unequal real roots in (-2,2).

When f(x) is an even function, the analytical expression on (-2,2) can be given according to the analytical expression on [-2,0].