@oristarA,
Quote:Which sentence sounds better?
1) ??Would you mind to explain something? ??
2) Would you mind explaining something?
As Aidan noted, Ori, number 2 is what you need for #1 isn't used in English. An 'ing form is used with 'would you mind'
Would you mind coming over?
Would you mind helping me with the dishes?
Would you mind carrying this?
Would you mind me feeding your dog a bone?
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Quote:??Would you like telling me why? ??
(The sentence above is better than "would you like to tell me why"?)
And with 'would you like', we use 'to' + infinitive.
Would you like to go to Rome?
Would you like to grab a bite to eat?
Would you like to see a movie?
Would you like to go bodyboarding?
Would you like to visit Jinmin?