If my opponent attacks my face-down Man-Eater Bug for example and he flips it as a result of battle and I chain it with Book of Moon, does Man-Eater go back face-down and gets flipped again by the same monster, saving my Bug or what?

no because the bug is flipped up in the damage step... nothing can be activated during the damage step unless it modifies the attack or defense of a monster. So you couldnt activate Book of Moon at all until before the monster is flipped up, or after the monster is destroyed

^
More or less the correct answer.
Think of it as battle. IF the monster destroys your bug (higher ATK) then your bug is killed.

ya but Quick-Plays can be activated during any phase right, i meen face-down...right?

no. not during the damage step. NOTHING can be activated during the damage step unless it would change the attack or defense of a face-up monster.

ya ever heard of Mirror Force, Magic Cylider, Negate Attack, Widespread Ruin, Sakuretsu Armor, Shadow Spell, Spellbinding Circle, Waboku, Nightmarte Wheel, Divine Wrath, etc...

they arent activated during the damage step. They are activated when your opponent announces an attack - during the Battle Step. Read the rule book.

o ok then say that, you just siad they cant be played at all!

yes i did... and they cant be activated during the damage step... only the battle step... there is a difference

okay lets go over the battle phase.

Battle Phase
The Battle Phase consists of 4 steps. The Start Step, Battle Step, Damage Step, and End Step.

heres what the official rule book version 5.0 says about the 4 steps:

1. Start Step: Declare that you are entering the Battle Phase. You and your opponent may both activate Quick-Play Spell and/or Trap Cards.

2. Battle Step: Select and announce 1 monster to attack with, and declare 1 of your opponent's monsters your target (the monster you wish to attack). You and your opponent may both activate Quick-Play Spell and/or Trap Cards.

3. Damage Step: Calculate the damage points of the designated monsters. If a monster has a Flip Effect, apply it immediately after damage calculation. However, a Flip Effect does not affect monsters that have already been destroyed as a result of damage calculation.

4. End Step: Resolve all battles by repeating the Battle and Damage Steps as many times as necessary, then declare an end to your Battle Phase. You and your opponent may both activate Quick-Play Spell and/or Trap Cards.

^ pages 25-26

MORE ON THE DAMAGE STEP:

During the Damage Step, only Quick-Play Spell Cards or Trap Cards that modify the Attack and/or Defense of a monster may be activated. IN addition, these cards can only be played before the Damage Calculation (page 28)

I know the difference between them :angry:

so, then you understand what i'm saying?