Two segments versus three
0169-4132 is a product NDC: labeler and product, nothing about package size. 0169-4132-12 is a package NDC: the same formulation in one specific commercial configuration.
Drug databases and FDA listing files are organised around product NDCs, because that is the level at which a drug has a name, a strength and a class. Reimbursement works at the package level, because payment depends on how much drug was in the container that was opened.
Why the mix-up happens
Search results, labels and reference sites usually show the product NDC, since it is the shorter, more memorable form. Someone copying it onto a claim gets a code that is real, resolves correctly in a lookup, and is nonetheless not billable.
The resulting denial usually cites an invalid or incomplete NDC, which reads as a data-quality problem rather than a wrong-level problem, so it often gets re-submitted unchanged.
Kits are the hard case
An adjuvanted vaccine or a reconstitution pack has an outer carton NDC and one or more inner component NDCs. The outer kit code is normally the billable one; submitting an inner component instead prices the component rather than the dose administered.