It's taken from ひぐらしのなく頃に OP (lyrics can be found here )
I know the meaning of each individual word, but I can't really understand how it works in this context: 鏡の中で蠢き伸ばしてくる無数の手で
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I think the main verb is the 伸ばす part. The phrase 手を伸ばす is used to mean "reach our your hands." Then the 蠢き that precedes it describes the way these hands are coming toward (that's where くる comes in) the indirect object who is not mentioned.
So basically the compound 蠢き伸ばしてくる would mean to come reaching out in a kind of creepy shaking/wiggling way.