why it is can't be To je mé tety medvěd
"mé tety" is the so-called non-agreeing attribute (they do not change as the noun changes its cases). Those should come after the noun.
Please help me to understand why the word order cannot be "To je mojí tety medvěd" Thanks!
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Could it be "To je moji tety medvěda"?
No. "mojí tety" is a non-agreeing modifier (does not follow the case and number of the noun) and hence should be after the noun. And it is medvěd, not medvěda. A specifically-female bear is medvědice.