To construct the box, squares of side length \( x \) are cut out from each corner of the tin. When these tabs are folded up, the height of the box will be equal to the length of the side of the square that was cut out.
Therefore, the height of the box is:
\[ \text{Height} = x \text{ inches} \]
So, the answer is:
The height of the box is \( x \) inches.