The value of x is 3.

Here is a bit of help to get you started toward the answer.

If the perimeter of the small square is "4x", then the length of its side is "x", and its area is x^2.

So the area of the red square is also x^2.

Now the side of the yellow square is 2x, and its area is then 4x^2.

This makes the side of the green square 3x, and its area is
9x^2

Continue in this manner to find the areas of each square, then add them together and set the sum equal to 6,426 and solve for "x".

Or perhaps you can think of another way......

Back to try some more.