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I simply cannot understand the notation used in this question:
I need to express this chord in 4-part, open or close position; I just can't seem to understand how the notation works. I know that this is a seventh chord; however, I don't think there's enough information to know what type of seventh chord it is.
Note: This is from my AP Music Theory homework; I'm not asking for an answer. I just want to understand the notation.
The notation builds up by intervals from the bass in close position (although you don't need to realise it in close position). For sevenths, you don't need all three intervals to specify: typically just the two most characteristic are used. In this case, you have an inversion of a minor seventh chord on ii that has a fifth and sixth from the bass in close position, that is, the first inversion where the third of the chord is in the bass. The usual convention is 7 for root position, 6/5 for first inversion, 4/3 for second inversion and 4/2 for third inversion.
The symbol is Roman numeral analysis with figured bass which is more than enough information to build the specific chord. It is telling you that the harmony at that point is a minor 7th (from the lower case of the roman numeral & the figured bass) built on the second scale degree (from the value of the Roman numeral) of Gb major (the note before the colon and the letter is capital so major) in first inversion (from the figured bass).
Brushing up on Roman numeral analysis and figured bass should be enough to help. MusicTheory.net has a very good lesson on the Roman numeral analysis of 7th chords and building chords based on that. I suggest starting there and if there are general concept questions about this notation that you still don't understand you can ask a follow up question here.
