diff --git a/xarray/namedarray/core.py b/xarray/namedarray/core.py
index f13c7e8d2c6..21bddf44e4e 100644
--- a/xarray/namedarray/core.py
+++ b/xarray/namedarray/core.py
@@ -597,12 +597,12 @@ def _dask_finalize(
         data = array_func(results, *args, **kwargs)
         return type(self)(self._dims, data, attrs=self._attrs)
 
-    def get_axis_num(self, dim: Hashable | Iterable[Hashable]) -> int | tuple[int, ...]:
+    def _get_axis_nums(self, dims: _Dims) -> tuple[int, ...]:
         """Return axis number(s) corresponding to dimension(s) in this array.
 
         Parameters
         ----------
-        dim : str or iterable of str
+        dim : tuple of str
             Dimension name(s) for which to lookup axes.
 
         Returns
@@ -610,14 +610,12 @@ def get_axis_num(self, dim: Hashable | Iterable[Hashable]) -> int | tuple[int, .
         int or tuple of int
             Axis number or numbers corresponding to the given dimensions.
         """
-        if not isinstance(dim, str) and isinstance(dim, Iterable):
-            return tuple(self._get_axis_num(d) for d in dim)
-        else:
-            return self._get_axis_num(dim)
+        return tuple(self._get_axis_num(d) for d in dims)
 
-    def _get_axis_num(self: Any, dim: Hashable) -> int:
+    def _get_axis_num(self: Any, dim: _Dim) -> int:
         try:
-            return self.dims.index(dim)  # type: ignore[no-any-return]
+            out: int = self.dims.index(dim)
+            return out
         except ValueError:
             raise ValueError(f"{dim!r} not found in array dimensions {self.dims!r}")
 
@@ -710,7 +708,7 @@ def reduce(
             raise ValueError("cannot supply both 'axis' and 'dim' arguments")
 
         if dim is not None:
-            axis = self.get_axis_num(dim)
+            axis = self._get_axis_nums(dim)
 
         with warnings.catch_warnings():
             warnings.filterwarnings(