How did the Third
Estate want to
vote?

They want to have their votes to be counted/worth more.

During the Estates General in 1789, Louis XVI gave the power to the Three Estates (First-Clergy, Second-Nobility, and Third-Everyone else) to decide on how to impose new taxes and to undertake reforms in the country. The King created a voting system where all the Estates get one vote. However, this system was unfair because the first two Estates would vote out the Third Estates(even though their Estates was 98% of the population of France). Thus, they wanted their vote to worth more.

It’s both true and false