I have a single object and I would like to put 6 of these same objects in a 2x3 shape, in a way that the edges touch perfectly.

Currently, I am doing it by hand, that is Ctrl-C , Ctrl-V then try to use Distribution and keyboard arrow movement to place them in the grid.

Problem is that using keyboard arrows to move objects, I end up with tiny bit of discrepancies.
So far "best" way i have found is create 3 of the same objects, distribute them evenly horizontally, then copy those 3 objects and try to align them vertically with arrow keys, but it is not a perfect fit!

What could be a better way?

The quickest way is to use tiled clones (Under Edit menu). Set rows 2, columns 3 and you can leave everything else at default, you will get clones perfectly one next to another. The original object will be hidden beneath the first clone, you can delete the first clone entirely. If you don't like having those objects as clones you can unlink them after you create them so they become just copies.

Use grid and snapping to grid when creating something with a fixed structure

… and Inkscape offers the 'Rows and Columns' dialog which allows you to easily arrange a selection of objects into a grid.

Thanks for the help!

Indeed, using tiled clone then using Shift-Alt-D to unlink clones(I have to adjust fill to each one of them) works much better than my "hands-on" method.