The solid below is made up of 1-cm cubes. How many more 1-cm cubes must be added to the solid to make it a cuboid measuring 4 cm by 3 cm by 4 cm?

1. Calculate the total number of 1-cm cubes needed for the target cuboid

Total cubes needed = $4 \times 3 \times 4 = 48$

2. Count the number of 1-cm cubes currently in the solid

Number of cubes in Layer 4 = $1$
Number of cubes in Layer 3 = $3$
Number of cubes in Layer 2 = $6$
Number of cubes in Layer 1 = $10$
Total existing cubes = $1 + 3 + 6 + 10 = 20$

3. Calculate the number of additional cubes required

Additional cubes = $48 - 20 = 28$