Slope-intercept form looks like this: y = mx + b
So, you want to get 'y' by itself on one side. To do this, subtract 4x from both sides to remove it. You subtract 4x because it eliminates it. You must do it to both sides because whatever you do to one side of the equation, you must do to the other.
4x + y = 6x - 1
-4x -4x
y = 2x - 1
y = 2x - 1 is your answer
Hope this helps!