Lord Gaṇeśa, the elder son of Lord Śiva and Pārvatī-dev, is considered as one who has one only one tusk, as he used the other tusk to write the great Mahābhārata that was dictated to him by Vyāsa. It is one of the reasons why he is called as Eka-danta. He is also called as Vakratuṇḍa, which literally means the one with a curved trunk. This is suggestive of discrimination between right and wrong. He thus teaches us to understand the two and to choose the right at all times in life. It further suggests flexibility in life to attain success. Furthermore, the elephant stretches its trunk to caress its young ones. Gaṇeśa also extends his trunk with compassion to those in distress.
This Gāyatrī mantra on Gaṇeśa honours him with these two names. Listen to it 12 times in the morning and 12 times in the evening to free you of any distress that may be bothering you.
oṁ tatpuruṣāya vidmahe vakratuṇḍāya dhīmahi | tanno dantiḥ pracodayāt