Yoma, 71b: 'Wherever the Torah writes "Sheish", the threads were six-fold. The Torah writes "Sheish" five times - by the tunics, by the turban (of the Kohen Gadol), by the hats of the Kohen Hedyot, by the pants and by the belt: Once for its intrinsic teaching, once to teach us that the threads should be six-fold, once that they should be twined together, once to include other Begadim by which 'Sheish' is not mentioned and once to teach us that all this is crucial - and renders the Beged Pasul if any of them is omitted. ¹

Ramban and Moshav Zekenim: It teaches us that the Kutones of the Kohen Hedyot was made of linen, just like that of the Kohen Gadol. And the same applies to the Mitznefes and the Avneit. ¹