Calculate Cuboid Dimensions: Finding Length of 4x3 Rectangles and 4x4 Squares Construction

To determine the feasability of a cuboid composed of two 4x3 rectangles and four 4x4 squares, we start by calculating the total surface area these would provide:

The total surface area contributes as follows:
- Two 4x3 rectangles: $2 \times 4 \times 3 = 24$
- Four 4x4 squares: $4 \times 4 \times 4 = 64$

The total surface area is $24 + 64 = 88$.

When forming a cuboid with dimensions $l \times w \times h$, the surface area should satisfy:
$2(lw + lh + wh) = 88$.

Now, let us examine possible dimensions that can result from the given face dimensions:

• Dimension 1: 4 (from the squares).
  
• Dimension 2: 3 (from the rectangles).
• Dimension 3 needs consideration from remaining panels.

Since using the given two 4x3 rectangles and four 4x4 squares in a valid arrangement providing 6 surface faces does not meet the criteria without repeating or extending beyond six faces, the random assembly of these square and rectangular panels cannot result in a valid orthogonal shape (cuboid).

Conclusively, this orthohedron is not possible.

Thus, the solution is that 'This orthohedron is not possible.'