I can look up the range of tempos that classify as moderate, but cannot find a source that tells me the specific bpm for:
Tempo (Speed): Moderate 4
Assuming the time signature is 4:4
The only really awkward thing about what you posted is the "Tempo (Speed):" part. It's as if the editor is treating this as beginner music, but then using a tempo designation that you would be more likely to see in professional show books. (Then again, this is a Berklee book...)
I consider this marking to be quite a bit different from plain old "Moderato". Most definitions of Moderato I've seen are 86-97 BPM. However, that is in a classical context. Popular contemporary music is usually treated differently, and indeed, some newer metronomes are indicative of what I might call "tempo inflation," shifting BPM numbers up across the whole range of definitions.
Anyhow, the thing to realize is that any tempo marking written out in words is giving you much more information than a simple metronome marking (BPM). Words have connotations of feel, and indeed should be contextualized within the time period they were written. If you're just trying to find a mapping from the words to a BPM, you're missing the point.
So, back to the question at hand. As I mentioned above, I disagree somewhat with how the editor has decided to print this tempo mark. The way I would expect to see it in a professional show book would be "Moderate Four," just written up in the corner where the tempo is supposed to be. No need for "Tempo (Speed):" (and indeed, I think his use of the numeral 4 causes some unnecessary confusion). What this tells us is:
Guess what! It's super-subjective! (But so are a lot of things in music!) For me (and without seeing the full piece of music), this means about quarter = 110, with the groove I described above. For you or your guitar teacher it might be different, but this doesn't mean there's no wrong answer! If someone with more experience than you says it should go one way, you should probably listen to them, because the reason all of this vocabulary exists is because it has useful meaning to the professionals that play this kind of music every day.
There is no standard "Moderate 4". For one thing "Moderate" is English while the normal language would be Italian, "Moderato". And incidentally more than half of the answers are for "Moderato", missing the fine difference. So that is a good indication that this is a non-standard thing to write over a score.
Then "Moderate 4" is a crutch since "4" is not really used as an indication of note length. Any sketch referring to a particular note value is going to use a note symbol, like "♩=80" for quarter notes at a speed of 80 per minute.
When the basis for a speed is the denominator of the time signature fraction, you don't really need to specify the reference at all.
So "Moderate 4" is likely intended to be helpful to beginners not really yet into score parlance and it suggests that whatever this was written with does not make it easy to put quarter note symbols into a heading.
Another option would be if you have an electronic keyboard with a button marked "Moderate 4" and the score is a school particularly for that keyboard. But since we are talking about guitars here, that is not a likely scenario.
Moderato is specifically vague. 108 to 120 bpm is the range. No classical music needs more than this 'guide' as that term 'moderato' is sufficient. I just hope your 'moderate' is in fact 'moderato'.
Most pop music will have a metronome mark, which is far more specific, although not often adhered to particularly.