The problem statement is ambiguous.  We assume the following will correctly describe the problem:

"A piece of posterboard has a length four times the width, then a 6 in piece is cut off the width, leaving with a piece of posterboard with the perimeter of 156 in.  What are the dimensions of the original piece of posterboard?"

let 'w' represent the original width, then '4w' represents the original length

perimeter = 2*width + 2*length

156=2(w-6)+2(4w)

click here to solve for the original width

w=16.8

4*16.8=67.2

Based on the above assumptions, the original posterboard's dimension was 16.8 x 67.2 inches.