To solve this equation, we can start by simplifying the left side of the equation.

First, let's multiply the two square roots together:

căn(x-2) * căn(4-x) = căn[(x-2)(4-x)]

Next, let's simplify the expression inside the square root:

(x-2)(4-x) = 4x - x^2 - 8 + 2x = -x^2 + 6x - 8

Now, let's substitute this simplified expression back into the equation:

căn[-x^2 + 6x - 8] = x^2 - 6x + 10

Now, let's square both sides of the equation to eliminate the square root:

[-x^2 + 6x - 8] = (x^2 - 6x + 10)^2

Expanding the right side of the equation:

-x^2 + 6x - 8 = x^4 - 12x^3 + 46x^2 - 120x + 100

Rearranging the terms and combining like terms:

x^4 - 12x^3 + 46x^2 - 120x + 100 + x^2 - 6x + 8 - 6x + 8 = 0

Simplifying further:

x^4 - 12x^3 + 47x^2 - 134x + 116 = 0

Unfortunately, this equation cannot be easily solved algebraically. You may need to use numerical methods or a graphing calculator to find the approximate solutions.