Hello, Fer,

If I understand the drawing, this is a rectangular box with height = 12, width = 6, and depth = x. It has 6 surfaces with a total surface area of 432 unit^{2}.

The 6 sides are comprised of 3 pairs. We can express the area of the three sides and then multiply each by 2 to obtain the total area:

The three expressions would be:

6x unit^{2}

12 unit^{2}

12x unit^{2}

Multiply each by 2 to include the second, identical side:

12x unit^{2}

24 unit^{2}

24x unit^{2}

Add these and set equal to 432 unit^{2}

12x + 24 + 24x = 432 unit^{2}

36x + 24 = 432 unit^{2}

36x = 408 unit^{2}

x = 11.3333 units

Bob