What does "favored by the entropy factor" mean exactly? Does it mean which direction does entropy increase? if so, I thought reverse reaction is the direction in which entropy increases because, as I said earlier, I thought breaking bond means increasing of entropy.
Any comment and help would be appreciated. Please help me guys!
"favored by the entropy factor" would mean that the reaction tends to be spontaneous (all other things equal) for a process in which the entropy increases. There's a statistical argument for why this is the case, but it seems like it's better just to leave it as axiomatic in your case.
The reason the reaction you gave is entropically favored in the forward direction is because more moles of gas are formed when going in the forward direction. Gas has a much higher entropy than a solid because it is significantly more disordered (there are a lot more equivalent ways to organize the molecules in a gas than a solid). Generally speaking the entropy gain by forming gases (gasses?) almost always surpass any entropy loss from other processes that might be going on in the reaction, so it's pretty safe to always conclude that if a process leads to more moles of gas, it's entropically favored. This doesn't necessarily mean it will be spontaneous, because you also have to consider the enthalpy.
Also: breaking a bond itself doesn't necessarily carry with it an entropic favorability. Sometimes breaking bonds can be entropically favored, sometimes it can be not entropically favored. It depends on changes that happen in the environment (the way products interact with nearby solvent molecules, etc.).