BUG: df.explode mulitcol with Nan+emptylist

doc/source/whatsnew/v2.0.0.rst

@@ -715,6 +715,7 @@ Reshaping
 - Bug in :func:`join` when ``left_on`` or ``right_on`` is or includes a :class:`CategoricalIndex` incorrectly raising ``AttributeError`` (:issue:`48464`)
 - Bug in :meth:`DataFrame.pivot_table` raising ``ValueError`` with parameter ``margins=True`` when result is an empty :class:`DataFrame` (:issue:`49240`)
 - Clarified error message in :func:`merge` when passing invalid ``validate`` option (:issue:`49417`)
+- Bug in :meth:`DataFrame.explode` raising ``ValueError`` on multiple columns with ``NaN`` values or empty lists (:issue:`46084`)
 
 Sparse
 ^^^^^^

pandas/core/frame.py

@@ -8844,7 +8844,7 @@ def explode(
         if len(columns) == 1:
             result = df[columns[0]].explode()
         else:
-            mylen = lambda x: len(x) if is_list_like(x) else -1
+            mylen = lambda x: len(x) if (is_list_like(x) and len(x) > 0) else 1
             counts0 = self[columns[0]].apply(mylen)
             for c in columns[1:]:
                 if not all(counts0 == self[c].apply(mylen)):

pandas/tests/frame/methods/test_explode.py

@@ -280,3 +280,24 @@ def test_multi_columns(input_subset, expected_dict, expected_index):
     result = df.explode(input_subset)
     expected = pd.DataFrame(expected_dict, expected_index)
     tm.assert_frame_equal(result, expected)
+
+
+def test_multi_columns2():
+    # GH 46084
+    df = pd.DataFrame(
+        {
+            "A": [[0, 1], [5], [], [2, 3]],
+            "B": [9, 8, 7, 6],
+            "C": [[1, 2], np.nan, [], [3, 4]],
+        }
+    )
+    result = df.explode(["A", "C"])
+    expected = pd.DataFrame(
+        {
+            "A": [0, 1, 5, np.nan, 2, 3],
+            "B": [9, 9, 8, 7, 6, 6],
+            "C": [1, 2, np.nan, np.nan, 3, 4],
+        },
+        index=[0, 0, 1, 2, 3, 3],
+    ).astype({"A": object, "C": object})
+    tm.assert_frame_equal(result, expected)