Question 886812
The sides of the piece of cardboard, before
cutting out the corners, are 
{{{ x }}} and {{{ x + 6 }}} cm
------------------------
After cutting out 2 x 2 squares from the corners,
The sides measure {{{ x - 2 - 2 }}} and
{{{ x + 6 - 2 - 2 }}}
----------------------
{{{ x - 2 - 2 = x - 4 }}}
{{{ x + 6  - 2 - 2 = x + 2 }}}
--------------------------
When the 4 sides are folded up, the height of
the box will be {{{ 2 }}} cm, so I can say:
{{{ ( x - 4 )*( x + 2 )*2 = 182 }}} cm2
{{{ ( x^2 - 4x + 2x - 8 )*2 = 182 }}}
{{{ x^2 - 4x + 2x - 8 = 91 }}}
{{{ x^2 - 2x = 99 }}}
Complete the square
{{{ x^2 - 2x + ( 2/2 )^2 = 99 + ( 2/2 )^2 }}}
{{{ x^2 - 2x + 1 = 99 + 1 }}}
{{{ ( x - 1 )^2 = 10^2 }}}
Take the square root of both sides
{{{ x - 1 = 10 }}}
{{{ x = 11 }}}
{{{ x + 6 = 17 }}}
----------------
The piece of cardboard measures 11 x 17 cm2
----------------
check:
{{{ ( x - 4 )*( x + 2 )*2 = 182 }}} 
{{{ ( 11 - 4 )*( 11 + 2 )*2 = 182 }}}
{{{ 7*13*2 = 182 }}}
{{{ 182 = 182 }}}