in 你家里有几个人 the possessive word de is omitted which often happens when you talk about family members or parts of the body 我的 手 疼 = 我 手 疼

I think you can memorize 的 "de" this way. 的 can be directly explained as " of"; " 's" and some NOUN nominatives like your my her his etc. anyway, as long as you think something belongs to somebody ( an attributive relationship), or something, you can type 的。 But, mind the words being modified ( the words after 的), of which part of speech has to be Noun. (Change 的 into 地 (di), while the words after it are verbs. Hope it helps but not worsen.

Hello! Well, actually"你的家里有几个人?"has the same meaning with "你家里有几个人?", and the "的" is usually omitted. They do both mean "How many people are in your family.". But if you add a time adverb"現在(now)"to the sentence becoming "你(的)家里現在有几个人?", the meaning will change to something like "How many people are there now in your house?" You might like to ask when the "的" can be omitted, well, there are no inflexible rules actually. Factors such as the noun following "的", context, mood,...etc ,would affect whether "的" is omitted or not. We can say: 我的家→我家 means my family or my house 你的家→你家 means your family or your house 他的家→他家 means his family or his house 我們的家→我們家 means our family or our house 你們的家→你們家 means your family or your house 他們的家→他們家 means their family or their house but not: 我的書 my book --X--> 我書(sounds weird) 你的床 your bed --X--> 你床(sounds weird) 他們的車 their car --X--> 他們車(sounds weird) However, you can ask: 我書咧? Where the hell is my book? 你床咧? Where the hell is your bed? 他們車咧? Where the hell is their car? 我的書呢? Where is my book? 你的床呢? Where is your bed? 他們的車呢? Where is their car? And in some cases, if "的" is omitted, the meaning changes as well: 你的豬 your pig 你豬! You are PIG! The omission occurs mostly in oral conversation or casual writing, and it's suggested you use "的" when dealing with formal occasions. I'm not sure whether you read Traditional Chinese, and the examples above are adopted from my everyday life in Taiwan, hope that helps!