Hi there,
Yes, you actually count DOWN 3 semitones (interval of a minor 3rd) from the major tonic note to get the tonic of the relative minor.
e.g. D major - count down three semitones (Db/C#, C, B,) ANSWER = B minor.
This is always how I teach my students, however, I do know that some teachers use the 4 semitones method but by that they mean that you have to count the note you are already starting on.
I find this too confusing as if you count the note you are already on then you are not counting down!
Hope this makes sense and is of help.
Best wishes,
Bigsymusic.
But the "4 semitones method" will give an incorrect result every time. Counting 4 down involves 4 chromatic notes downwards inclusive of the major tonic. A single note is not a semitone.