Neutrosophic set theory is an efficient framework used in real-world applications like image processing, pattern recognition, expert systems, and decision-making to handle imprecise, ambiguous, and incomplete data. The neutrosophic number is a particular case of the neutrosophic set that helps to handle uncertainties and vague information, which is one of the most emerging research fields. In this paper, we have presented the generalized non-linear hexagonal neutrosophic number with asymmetry (GNHNNA), and the ranking method for GNHNNA is also obtained using values and ambiguity. The significant advantage of values and ambiguity is that the ordering of this generalized number can be established without computation of ( \( \alpha , \beta , \gamma \) )-cut. Further, related theorems and arithmetic operations of GNHNNA are discussed.