A fielder took the catch and made two steps backward and made contact with the boundary rope.
Will it be declared as a six or four?
As per law 19 (Boundaries)
(c) A Boundary 6 will be scored if and only if the ball has been struck by the bat and pitches beyond the boundary. The ball is to be regarded as pitching beyond the boundary even though before it has pitched, a fielder
(i) catches it within the boundary but either has some part of his person touching the boundary or grounded beyond the boundary when he catches the ball or, after catching it, subsequently touches the boundary or grounds some part of his person beyond the boundary while carrying the ball but before completing the catch.
So it will be considered as a SIX because the ball didn't touch the ground at all.
The act of making the catch, or of fielding the ball, shall start from the time when the ball first comes into contact with some part of a fielder’s person and shall end when a fielder obtains complete control both over the ball and over his own movement.
if he steps out deliberately after having obtained completed control then it's out, if he steps out accidentally as part of the movement of the catch then it's a six.