"Let the linear expression we need to add be:" \qquad L.
"So, from the question, we want" \ L \ "to achieve the following:"
\qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad L + ( -4 y + 2 ) \ = \ y.
\qquad :. \quad \ L + ( -4 y + 2 ) - ( -4 y + 2 ) \ = \ y - ( -4 y + 2 )
\quad :. \ \ L + color{red}cancel{ ( -4 y + 2 ) } - color{red}cancel{ ( -4 y + 2 ) } \ = \ y + 4 y - 2
\qquad :. \qquad \qquad \qquad \qquad \qquad \qquad \ L \ = \ 5 y - 2.
"This is our answer."