You probably can't, because your parent comment's figure is too large and too precise.

You can get some maps at e.g. <https://en.wikipedia.org/wiki/List_of_nearest_stars_and_brow...> and more if you explore through the cited papers.

There are 10 known stars or star-systems within approximately 10 light-years of our local star (Proxima Centauri, the Alpha Centauri triple, Barnard's star, Luhman 16 in Vela, W0855 in Hydra, Wolf 359 in Leo, Gilese 411 in Ursa Major, the Sirius binary, and the UL Ceti / BV Ceti binary and right on the edge of our 10 light-year bubble V1216 Sagittari). There are 93 within 20 light-years. These counts include multi-star systems.

I write "known" because there may be dim stellar objects we haven't found yet.
The double in Vela are both dim brown dwarfs, much smaller than the sun, and were only discovered in the last decade or so, despite being less than seven light-years away. Brown dwarfs are hard to spot. Red dwarfs become similarly hard to spot at a distance of only 20 light-years.

Without descending into power-law discussions (although see <https://news.ycombinator.com/item?id=32613762> if you are curious and want to think about the density of dim dwarfs vs bright naked-eye stars), we can just accept that the density of stars within 100 light-years is likely very similar to that within 10 light-years and within 20 light-years.

The volume of a sphere goes 4/3 * pi * r^3. A 20 light-year (ly) sphere has 8 times the volume of a 10 ly sphere. We have roughly 10 stars vs roughly 100 stars, so that tracks roughly. Extrapolating and taking only orders-of-magnitude estimates of star counts, a 100 ly sphere has 125 times the volume of a 20 ly sphere, so we would expect the star-count to rise from roughly 100 to roughly 10000 stars. That's much less than half of the almost sixty-thousand number that your comment's parent suggests.

To multiply the rough estimate based on the 10-ly and 20-ly count by between about four and six to match the "59,722" figure we would have to introduce one or more screening mechanisms or properties to hide so many more stars. Properties include intrinsic dimness and low mass. If we require that stars are self-luminous that means they must be massive enough for nuclear fusion in their cores, so at the lowest end that means brown dwarfs like the ones mentioned a couple paragraphs above, somewhat heavier and brighter red dwarfs, and so forth. Screening properties would involve arranging these unseen stars in such a way that they eclipse one another, are hidden behind brighter dust, and have low proper motion about the "local standard of rest" average motion stars moving in our part of the Milky Way. Not only do we have a sudden jump in the volume-to-mass relationship compared to 10 and 20 light-years, we would also have to cut off the volume-to-mass relationship not too far outside the 100 light year bubble, or dramatically change the shape of our own galaxy compared to that of spiral galaxies, and our understanding of the proper motion of the Andromeda galaxy towards us. We also have to deal with the results from gravitational micro-lensing surveys (e.g. from MACHO hunting), and the study of the fast orbits of stars in the Milky Way's central parsec, neither of which supports large numbers of dim-but-considerably-bigger-than-Jupiter masses lurking in our galaxy.

If we go the other direction and start with the evidence that we are in a spiral arm of a galaxy like Andromeda, and that the "thin disc" stellar density is about 0.004 per cubic light year (<https://en.wikipedia.org/wiki/Stellar_density> and the recent <https://arxiv.org/abs/2207.03492> which maps comparable-scale variations in the stellar density in the Milky Way's thin disc), then in a 100-light-year sphere having a volume of about 4.2 million cubic light years we end up expecting a little fewer than seventeen thousand stars.

Consequently, unless there's something almost uniquely special happening around 30-100 light-years from here, a much better estimate for the star-count within 100 light years is twelve thousand plus or minus five thousand. Note that this is a much less precise figure than the one given upthread.