The honest answer is that it takes more than one appointment, and anyone who tells you otherwise is selling you a session that will damage your hair.
Box dye is formulated to work without a stylist, which means it deposits far more pigment than we would use, and it deposits the same amount everywhere. Two years of it means your ends are holding several layers of colour while your roots are holding none. Lifting all of that in one sitting is what produces the breakage people arrive here trying to fix.
What we normally do instead is spread it over two or three appointments six to eight weeks apart, pulling the old pigment out gradually and rebuilding the bond in between. It is slower and it is less satisfying on the first day. It also leaves you with hair you can still brush.