Nets and Surface Area

The surface area of a solid is the total area of its outside: how much paper it takes to wrap it with no overlap. Cut a box along some edges and fold it flat, and you get its net, six rectangles in one piece. The surface area is the area of the net.

The faces come in three equal pairs. This box has a top and a bottom of $4\cdot 3 = 12$ each, a front and a back of $4\cdot 2 = 8$ each, and two sides of $3\cdot 2 = 6$ each. Together: $2\cdot \left(12+8+6\right) = 52$.

The rule is Surface area of a cuboid: $SA = 2\cdot \left(l\cdot w+l\cdot h+w\cdot h\right)$. A surface area is an area, so its unit is square: cm², not cm³.