"Which bag is yours?"
Thank you. Always nice to find out where Duo is legit and where it's going a bit wrong. (And goodness knows word order in any language is seldom THAT strict!)
One other question: how important is "是" in that sentence? Normally, when someone is talking about an adjective/modifier, we're not supposed to use it as the verb. For example, "I am a student./ 我是学生。“ vs "I am busy./ 我很忙。“ So isn't "你的“ basically a modifier, not a noun? So can't we drop "是“ from that sentence?
是 is necessary in that sentence. 你的 usually serves as a modifier, but here it's a substantive, just like 学生, and 是 turns it into a predicate the same way.
(Sorry for the terminology. I'm using 'substantive' for what linguists call 'noun phrase', because it isn't necessarily more than one word, and it doesn't have to include a noun. It's what we call terms that can be the subject of a sentence, object of a verb, etc.: 'a big dog', 'my hair', 'it', 'yours', 'Albania', 'the middle-aged'.)
In English, we have 'your' for the modifier and 'yours' for the substantive:
Right: Which bag is yours?
Wrong: Which bag is your?
Right: Your bag
Wrong: Yours bag
But in Chinese, 你的 does both jobs. Word order and 是 tell you which.
More terminology and clarifications. I promise this isn't just nitpicking, it's relevant to understanding grammar.
'Adjective' is what a word is. 'Modifier' is a job it has.
'Modifier' is not the only job adjectives do.
Adjectives are not the only noun modifiers.
'Verb' is what a word is. 'Predicate' is a job it has. Other types of words can be predicates too, but depending on the language they may need some grammatical support for it.
'Red' is an adjective. In 'the red wheelbarrow' it's a modifier. In 'the wheelbarrow is red' it isn't, it's part of the predicate. But English requires 'is' if you want to use an adjective as predicate.
It might be better to think of 忙 not as an adjective, but as a verb. (A verb of state, not a verb of action. Those exist. 'To stink' is an example.) Not 'busy' but 'be busy'.
You can use it as a predicate all by itself: 你忙吗? And when you use it as a modifier, you need 的 to link it: 忙的人爱这个东西, 'busy people love this thing'. Both of those are verb-like behaviors: 你吃水果吗？吃水果的人爱这个东西。'Do you eat fruit? Fruit-eating people love this thing.'
OK, so what's 很 for in 我很忙 then? It's a hint. It strongly suggests that what's coming up next is the predicate. But it's not mandatory the way that 'am' is mandatory in 'I am busy'. 很 isn't 'is'.
是 isn't 'is' either. 'Is' has a bunch of different jobs. It turns adjectives into predicates (no Chinese equivalent), it turns locations into predicates ('A big cat is inside my wardrobe', which overlaps with the functions of 在, and BTW it is probably best to think of 在 as verb-like 'be at' too), it turns substantives into predicates (that's the only part that overlaps with 是).
It's particularly confusing when 袋 actually means a pouch / bag / sack / pocket,
while 包 means to cover / to wrap / to hold / to include / to take charge of / to contract (to or for) / package / wrapper / container / bag / to hold or embrace / bundle / packet
I can only advise that 包 is the term more associated with a hand bag which is usually written as 手包, or shǒu bāo = hand bag