The claim recurs constantly in esoteric writing: the equinox precesses one degree every seventy-two years, the ancients knew it, and seventy-two is encoded in myth and monument as a marker of that knowledge. Two of those three statements need correcting.
The arithmetic is roughly right. The full precessional cycle is about 25,772 years, which gives one degree in about 71.6 years. Seventy-two is a rounding, and 72 x 360 gives 25,920 years, the figure usually called the Great Year in this literature. It is a tidy number rather than the measured one.
The ancient knowledge is not there. Precession is first described by Hipparchus in the second century BCE, who put it at not less than one degree per century, a rate implying a cycle of at most 36,000 years. Ptolemy adopted one degree per century in the Almagest, and that inferior figure remained standard in Western astronomy for a thousand years. No surviving ancient text gives seventy-two years per degree. Medieval Islamic astronomers improved the value substantially; the modern figure is a product of long-baseline observation.
The idea that pre-Hipparchan cultures encoded precessional numbers, 72, 432, 25,920, in myth comes from Hamlet's Mill, published by Giorgio de Santillana and Hertha von Dechend in 1969. The book was severely criticised by historians of astronomy on publication for selective use of sources and for treating numerical resemblance as evidence, and it has never been accepted scholarship. It remains the ultimate source of most claims of this kind, usually at several removes and without attribution.
Seventy-two has genuine and interesting uses. Precession is not one of them.