There is nothing wrong with "those". I would change ballet at the end to "ballets".
Student or Learner
What's wrong with the word "those" in this sentence, why and what is the correct word that should be put instead?
(An internationally famous ballerina, Maria Tallchief demonstrated the the quality of ballet in North America could equal those of the ballet in Europe.)
In this usage, "quality" is uncountable, so the singular that is appropriate.
I don't think it's necessary to use the plural to talk in such general terms about ballet in Europe, especially as this passage compares the ballet on one continent with the ballet on another.
But it isn't in the OP — correctly so. I agree with J&K that 'that' is the correct pronoun in this case.
Ran mohd, please note that your quoted sentence should be in inverted commas – not brackets, and that there should be a comma after 'Maria Tallchief'.
It depends on whether you consider "ballet" to be "a performance by ballet dancers" or simply the form of dance known as "ballet".
If it's the former, you could say "the ballets of Europe". In that case, I would say "... the quality of ballets in North America could equal that of those in Europe". ("That" refers back to "quality" and "those" refers to "ballets").
If "ballet" is used for the form of dance, I would say "... the quality of ballet in North America could equal that [of ballet] in Europe".
Remember - if you don't use correct capitalisation, punctuation and spacing, anything you write will be incorrect.