: My hand is too small to play a section of the piece I've been learning The Second Waltz, and there is part I can't play. As you can see, the bass has notes more than an octave away from each other at times. My hands can

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You can hold the lowest notes -- the dotted half notes -- with the pedal, which will free up your hand to move to the upper chords.
Also, in the penultimate bar of your example, you could play both the F and G with your thumb if you can comfortably reach it.

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I am 12, with very small octaves, but now I can play octaves with 9 notes, when a year ago, I couldn't do one octave. The best thing to do is buy multiple pencils, and cut them to just the perfect size to where it hurts a little, and bind the pencil to your hand and between your first and fifth finger

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This arrangement of a Waltz by Shostakovich is a simplification and you are not asked at all to play like it is notated: e.g. you can play the r.h. without octaves. If you play it on a draw bar or a keyboard without sustain function you can play the note B in the last chord of the 2nd phrase with the r.h. between the two F.
My advice is to play it as written, holding the G in the bass and jump to the two upper notes, as this is a good practice anyway to improve your hands skipping on the keys - and if you have it, using the sustain pedal.
Finally you want to make progressions and one day your hands my be less small and there will be many other situations where you will need to play a decimes like this.

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This is one reason why every piano has a sustain pedal - the one on the right. Press it when you play the first note in the bar, and keep it down until you play the first note in the next bar. Repeat as needed.
Since all the notes in each bar belong to the same harmony (chord) it will sound good, it will flow, and give you chance to move your hand from the lower note to the dyad above.
If you're lucky enough to have a piano with a middle pedal that is not just a quiet practice pedal, but a sostenuto pedal, you could use that instead. It works nearly the same, except it holds onto only the note played while it's pressed - others will be played normally.
The sostenuto pedal is common on pianos on the left of the Atlantic, rare on the right.