Question

How do I solve this?

Answer 1

Answer is 132 white boxes.

 The designs are increasing by 2 x 2 each time.

Design 1 is 2 x 2, 

Design 2 is 4 x 4, 

Design 3 is 6 x 6, 

Design 4 will be 8 x 8
Design 5 will be 10 x 10

Design 6 will be 12 x 12 for a total of 144 boxes.

The diagonal of shaded boxes will be 12 shaded. 
So 144 - 12 = 132 white boxes.

Answer 2

So, what i noticed is that there is a pattern regarding the grayed blocks. The first one starts off with 2, then 4, then 6. It is adding 2 each time, ex; 2+2+4, 4+2=6. The answer would be that the sixth one would have 12 grayed blocks.