Especially when looking at puzzles, always look for forcing moves (like checks) because it forces your opponent to react and makes it easier to calculate for you. In this case, checks can be done by the queen or knight.

• Nd5+ just blunders a Knight.
• Qe4+ loses the Queen.
• Qd3+ doesn’t accomplish much after a move like g6.
• But Qc2+ not only has eyes on the King, but also the Rook on a4.

This forks the Rook and King and forces Black to lose their rook after Qxa4. Rb8 like you suggest does not win any material, and is not forcing your opponent to make a specific move. Hope that helps. ---

Qc2+ forks the rook on a4 and the king, so black must either move the king to the back rank where white's rook can attack it or otherwise offer the Queen ...Qb6 (which is what the computer plays). Could also play g6 but either way, by playing Qc2+ and forking the rook in check you will play Qxa4 and take the enemy rook on the next move and black is pretty much done

Usually every time you feel like you don't get the solution, as it seems there's a better move, it's because you're missing some counter to the "better" move. It gets easier with time to spot those moves early on, but the harder the puzzles get the harder it becomes. It never ends. Welcome to chess!

Why would Rb8 force Qf5?

The solution given by lichess nets you a rook, I don't see a way to take the black queen