“Humble” VS “Modest”
Modest describes the personality trait or behavior of not flaunting oneself, talking oneself up or putting oneself on display. Modest behavior can be a response to compliments, praise or follow an achievement. Modesty can also manifested physically (for example, "dressing modestly", "modest accessories", "modest smile").
In contrast, "humble" refers specifically to a person's inner state and feelings. A humble person who has a low view of his own abilities. He will always view himself as weak in that area, even if he is not. A person is humble when he is willing to accept or respect another's authority, intellect and wisdom, or superiority without trying to challenge it or trying to assert oneself.
In summary, being modest refers to your behavior, being humble refers to your ego and both of the two are positive values.
One more point, as I read humbleness and humility are synonyms. They mean exactly the same thing: the quality or condition of being humble.
1. Accepting a Compliment with Humility
Peter: Max, everyone has been telling me how much they like working for you on this project.
Max: Nah, I’m a tyrant, they’re all just afraid to say so.
Peter: No really, there are people volunteering here today solely so they can work for you.
Max: I’ll bet they would switch departments in a minute if I would let them off the leash.
Peter: Max, seriously, the crew wants you to know how much they are inspired by your leadership.
Max: It’s all God’s doing, a trained ape could do the job I’m doing.
2. Accepting a Compliment with Modesty
"Your souffle is exquisite!"
"Thank you, I'm glad you enjoyed it."
"Your brooch is adorable."
"Why thank you! I was just noticing your boots, what a great color."
I hope that will help) I only did a research and came up with a combination of the highlighted answers.