Longer back-rank combinations is lesson 6 of 6 in Back-rank mates, a checkmate course suited to players rated around 900 (beginners). Several pieces can guard the back rank. Keep checking along it, exchange the defenders one by one, and the last check is mate. It has 10 interactive exercises: 10 calculated lines from real positions. You play every move on a board and get feedback straight away. The lesson is free.
What you practise
Black to move: mate in 3. (3 positions)
White to move: mate in 3. (3 positions)
Black to move: mate in 4. (2 positions)
White to move: mate in 4. (2 positions)
Worked examples
Black to move: mate in 3. 1...Re1+ 2.Kg2 Bf1+ 3.Kg1 Bh3#. The rook mated on e1: the king was shut in on the back rank by its own pawns. Mate in 3.
Black to move: mate in 3. 1...Qb1+ 2.Rc1 Qxc1+ 3.Qd1 Qxd1#. The queen mated on d1: the king was shut in on the back rank by its own pawns. Mate in 3.