Hi
First, duplication of the chromosomes means duplication of the DNA, which is called replication, and happens before mitosis, in the S phase (which is part of the interphase, not of mitosis).
To the point: your problem comes from the fact that a duplicated chromosome is still called one chromosome. Indeed, what you can see under the microscope, the karyotype at metaphase, is always formed of duplicated chromosomes (before metaphase the chromosomes are diffuse i.e. chromatin and not visible as distinct shapes or bodies under microscope).
So, 46 chromosomes (23 pairs because they look similar in pairs) before replication become 46 chromosomes after replication, only these now have 2 chromatids rather than one (but you cannot see the chromatids). During mitosis each chromosome (double, 2 chromatids) will split in two identical chromosomes (a single chromatid) and so each daughter cell gets 46 chromosomes.
Remember: mitosis does not change the 2n number in a cell.