The process is mitosis.
It is a kind of cell division where all the daughter cells are genetically identical to its parents cell, same with 2 sets of chromosomes.
The process must be mitosis because all cells in your body (except for gametes) has the same amount of chromosomes, which is 46 for humans.
Mitosis also ensure that you are still yourself when you're growing up, not having for example blue eyes in 5 and brown in 10 years old. All the alleles are identical.