What does facsimile mean?
1 : an exact copy A facsimile of the world’s first computer was exhibited at the museum. 2 : a system of transmitting and reproducing graphic matter (such as printing or still pictures) by means of signals sent over telephone lines.
Which pronunciation of either is correct?
Using English phonetics, [ EE-ther ] and [ AHY-ther ] are both correct. As a side note, giving “th” a phonetic Z (or S or F or D) sound is a common mispronunciation that can be corrected with practice.