You didn't specify what you're being asked to calculate the "total area" of. If it's the total area of the walls and the ceiling, then obviously the fact that you want to paint them twice doesn't change that area. On the other hand, the question might be about the total area of paint covers to be applied. That would make sense for instance if you want to figure out how much paint to buy, since the amount of paint you need is proportional to the total area of paint covers you want to apply. If you want to paint surfaces with a certain total area twice, then the area of the paint covers to be applied is just twice the total area of the surfaces to be painted. However, from the answer you give, it seems that you're being asked to calculate the total area of the walls and the ceiling; in that case it's irrelevant how often you intend to paint them.
Regarding your attempt at calculating the surface area: You need to think more about the meaning of the terms "length" and "width". You're mixing up two different contexts in which these occur. When you calculate the area of a rectangle as "length times width", these terms refer to the two dimensions of the rectangle, independent of its position or orientation in space. By contrast, when we talk about the dimensions of a room, we speak of the room's length, width and height, meaning, respectively, its longer horizontal dimension, its shorter horizontal dimension and its vertical dimension. You equated these different meanings of the terms and just multiplied the length and width of the room.
What you actually need to do is to add up the areas of all the rectangles forming the four walls and one ceiling of the room. These will all be the product of the length and width of those individual rectangles, but these dimensions will be different combinations of the length, width and height of the room. Just go through all the walls and the ceiling and figure out which of the three given dimensions form the two dimensions of each of the rectangles.