The perimeter of the bottom surface of a rectangular wooden box is 16 decimeters, and the surface area is 78 square decimeters

Let the bottom of this wooden box be x in length and Y in width
From the meaning of the question: 2 (x + y) = 16, x + y = 8 (1)
2xy+2(3x+3y)=78 ,2xy+6(x+y)=78 ,xy+3(x+y)=39.(2).
xy+3*8=39.
Xy = 39-24 = 15 (square decimeter) --- that is the demand

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