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Chess puzzles:

White to move

That last one is quite difficult because obviously black has the upper hand. First off, moving the white knight (on F2) out of the way would be a huge mistake (without a threat to black) because black gets a free queen on E2. You could aggressively go after the black rook on G2 (using your queen on E2), but then you'd have to be aware that the black queen on H4 will more than likely capture the hanging pawn piece (on G5) and place your king (on D2) into check, thus attacking the white rook (on D8) at the same time. This is known as a "Fork", which is a pretty basic, yet nasty tactic in the game.

Sure, you could move the King out of the way towards the back file (D1 or E1), but then this would also cause problems as the black rook on G2 will end up taking the knight on F2 while the queen on H4 is ready to attack and protect, simultaneously. Obviously, moving the king towards C1 would be a rookie mistake because the black queen on H4 will still Fork you. At that point, you'd have no choice but to shield the king by moving the white queen (on E2) to either D2 or E3. The aftermath is that you'd be down by 6 points.

The ultimate goal is to avoid getting forked because you can survive with one less point, but not with 6. Also, you're probably thinking that moving your white rook from D8 to E8 seems like the wisest idea because you're potentially preparing to block a future check from G5 to D2. However, the aftermath is that the black rook on G2 will snatch your white knight on F2, while being defended by the devious black queen on H4. The aftermath is that you'll end up in check by the black queen on H4 to F2.

At this point, you're probably thinking: No matter what I do... I'm either getting forked, or losing a valuable piece (the white rook on D8). So, ultimately, if this were me in this situation, I'd probably just advance my white queen from E2 to E7. Why? - Because not only are you preventing a dangerous move from happening, you're essentially avoiding losing your white rook on D8. Unfortunately, you'd still be sacrificing the white knight on F2, but at least you can prepare to get the white king (on D2) to safety on C1. Your white queen on E7 is now guarding the pawn on G5.

After the white queen has moved from E2 to E7, DO NOT get greedy by aggressively going after the black rook with your king moving to E1. If you do, then they can turn this into a "Discovered Check" by moving the black rook from F2 capturing a white pawn (which is now a hanging piece) on C2, thus allowing the black queen on H4 to check you. This is a "Discovered Check". This can get ugly quick because black can prepare to trap you into a check using the black queen and rook. The statement in red is ultimately what you want to accomplish.