In both cases, one original cell splits – and stays split. The first answer’s reference to “meiosis” is the part about any cell becoming two cells – the 46 chromosomes each replicate, and by a mechanism which cell biologists surely have a name for (if that name isn’t already meiosis) the cell membrane pinches, and two cells exist. Each one has 46 chromosomes and a nucleus.
Sperm and egg cells skip the “copy” part, and when there are two cells, each has 23 chromosomes. Birth defects sometimes occur due to separation errors, e.g. one cell may have BOTH Chromosome 22’s – if this cell results in a baby, it will have Down Syndrome. Other separation errors can result in two or zero X or Y chromosomes, making 22 or 24 chromosomes and resulting in a baby with nonstandard genital plumbing.
As to correctly, the “correctly” part begins with cell division, where each cell gets one copy, thus an original 46 chromosomes becomes 92 before the cell splits in half. Egg and sperm cells do the same, but 46 stays 46, i.e. each half comes away with 23.
And MOST of the time, there are no org-chart errors.