The breadth of the room = 6 cm
Since the length of the room is twice its breadth
Then
Length of the room = 2 times 6cm = 12cm
The height of the room = 4cm
Since the shape of the room is a cuboid
The surface area of a cuboid is given as
[tex]SA=2(lh+lw+hw)[/tex]Substitute l = 12, w = 6 and h = 4 into the formula
This gives
[tex]SA=2(12\times4+12\times6+4\times6)_{}[/tex]Simplify the expression
[tex]\begin{gathered} SA=2(48+72+24) \\ SA=2(144) \\ SA=288 \end{gathered}[/tex]Therefore, the total surface area of the room is
[tex]288cm^2[/tex]