Side areas
The box in the image has six sides, each one consisting of rectangles
Note the sides come in pairs of equal areas
For example, the front and the back sides have the same dimensions, thus their areas are equal. Let's calculate them
Area of front side = 12 in * 2 in = 24 square inches
The sum of the front and back areas is:
2 * 24 = 48 square inches
Now for the lateral sides. Again, we have two similar shapes with identical areas:
Area of one lateral side = 14 in * 2 in = 28 square inches
Area of both lateral sides = 2 * 28 = 56 square inches
Finally, the top and bottom areas are equal:
Area of top side = 12 in * 14 in = 168 square inches
Area of top and bottom sides = 2* 168 = 336 square inches
The total area is
48 + 56 + 336 = 440 square inches
Henry has to paint 440 square inches