Audio gen. RF harmonics

I am hoping some mathematical genius can help me with this. I read of
a process whereby _specific_ harmonic frequencies can be added to a
fixed RF carrier by mixing it with an audio frequency. Both are
initially sinewaves, of course.

What is the mathematical basis for achieving this?

As an example, say one wants to add a 1.6MHz spectral component to a
fixed 4.6MHz carrier. What frequency within the audio range would
achieve this, and how is it determined.

Thank you greatly for any insight on this matter.

Mark Jennings
.