On each carbon three methyl groups are present in gauche conformation. A pair of methyl groups (methyl groups present on adjacent carbons) can cause one gauche interaction. So total we have 3 pairs of methyl groups. Therefore total 3 gauche inteteractions present. From this we have to consider only 3 methyl groups. Not 6 methyl groups.
I'm not even sure if I drew the structures correctly, so please double check that as...