Learn Polish: Cały motek włóczki mi się zaplątał. - The whole skein of yarn got tangled for me.

In Polish, using the dative case pronoun mi here creates what is called a dative of disadvantage. It shows that the yarn getting tangled affected you personally and unexpectedly, very similar to saying 'The yarn got all tangled up on me' in conversational English.

Why are the short words mi and się placed right after włóczki?

mi and się are clitics, meaning they do not carry their own voice stress. They naturally group together and usually take the second logical position in a clause. Here, they follow the entire subject phrase Cały motek włóczki (the whole skein of yarn).

Could I use the long form mnie instead of mi in this sentence?

Not naturally, because mnie is used for emphasis or at the absolute beginning of a sentence. Here, you are just stating what happened, not contrasting yourself with someone else (like 'It tangled for ME, not for you'), so the unstressed form mi is the natural choice.

Why is włóczki in the Genitive case?

It translates to 'of yarn'. When one noun describes another by answering 'of what?' or 'whose?', the second noun takes the Genitive case. The base dictionary form is the feminine noun włóczka.