Colloquially it's called a "double fianchetto." I don't believe it has a formal name, although you could look up variations of both openings that have that fianchetto: Owen Defense (1. e4 b6) and Modern Defense (1. e4 g6).
What is this Opening/Defence ?
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What is this Opening/Defence ? How do you counter this ? I have run into this a few times and I lose handily.