Lord Śrī Kṛṣṇa had two arms, and why He is designated as four-armed is explained by Śrīdhara Svāmī. Both Bhīma and Draupadī held opposite views about killing Aśvatthāmā. Bhīma wanted him to be immediately killed, whereas Draupadī wanted to save him. We can imagine Bhīma ready to kill while Draupadī is obstructing him. And in order to prevent both of them, the Lord discovered another two arms. Originally, the primeval Lord Śrī Kṛṣṇa displays only two arms, but in His Nārāyaṇa feature He exhibits four. In His Nārāyaṇa feature He resides with His devotees in the Vaikuṇṭha planets, while in His original Śrī Kṛṣṇa feature He resides in the Kṛṣṇaloka planet far, far above the Vaikuṇṭha planets in the spiritual sky. Therefore, if Śrī Kṛṣṇa is called caturbhujaḥ, there is no contradiction. If need be He can display hundreds of arms, as He exhibited in His viśva-rūpa shown to Arjuna. Therefore, one who can display hundreds and thousands of arms can also manifest four whenever needed.
When Arjuna was perplexed about what to do with Aśvatthāmā, Lord Śrī Kṛṣṇa, as the very dear friend of Arjuna, voluntarily took up the matter just to make a solution. And He was smiling also.