How many new cells are produced from each parent cell during meiosis?

The answer is 4 new (daughter) cells.

In meiosis, it produces 4 daughter cells which are genetically different from both the parent and the other daughter cells.
the parent cell first duplicates its chromosomes, just like mitosis (the kind of division that leads to 2 genetically identical daughter cells) . Then it divides, leading to 2 genetically identical daughter cells. But this does not end here. The 2 daughter cells further divides into total of 4 daughter cells, but without duplicating the DNA. That's why, the daughter cells has different DNA materials.
These daughter cells has half of the parents chromosomes, and we call them haploid.

Haploid cells are usually common in gametes. When an organism reproduces sexually, 2 gametes fuse together and leads to diversity.