China arrived at sixty independently and for a different reason. The ganzhi cycle pairs ten Heavenly Stems with twelve Earthly Branches. Since the stems and branches advance together and pair only in matching parity, the combination repeats after sixty steps rather than a hundred and twenty, sixty being the least common multiple of ten and twelve.
The cycle is old and its attestation is firm. Shang dynasty oracle bones of the late second millennium BCE use it to count days, and complete sixty-cycle tables are inscribed on bone. Application to years is much later, becoming standard in the Han period, and the cycle has run continuously since; a person completing their sixtieth year completes a full cycle, which is the basis of the significance attached to the sixtieth birthday across East Asia.
The twelve branches are also the twelve zodiac animals, and the ten stems pair with the five phases, wood, fire, earth, metal, water, in yin and yang forms, so any year in the cycle carries an animal and a phase: a wood dragon year, a metal rooster year. Those combinations recur every sixty years, not every twelve, which is why the popular presentation of the Chinese zodiac as a twelve-year cycle is a simplification of a sixty-year one.
There is no evidence of contact between the Babylonian and Chinese systems. Both converged on sixty because sixty is the smallest number that reconciles the small factors people actually count with, and that convergence is a fact about arithmetic rather than a sign of a shared source. Claims of transmission between the two should be treated as unsupported.