Śrīla Prabhupada: “Regarding your question about the picture of Lord Caitanya with six arms: This form was shown to Ramananda Roy, and Sarvabhauma Bhattacarya. This is called Sadbhuja Murti. This Sadbhuja Murti is worshiped also by the devotees of Lord Caitanya, and especially the Murti is situated in the temple of Jagannatha Puri. Sometimes when you may go to India and visit the temple of Jagannatha, you will find this Murti.”
(Letter to: Madhusudana, July 29, 1968, Montreal)

Śrīla Prabhupada: “Lord Śrī Rāmacandra is so kind and merciful to His devotees that He is very easily satisfied by a little service rendered by anyone, human or not. This is the special advantage of worshiping Lord Rāmacandra, and there is the same advantage in worshiping Lord Śrī Caitanya Mahāprabhu. Lord Kṛṣṇa and Lord Rāmacandra, in the manner of kṣatriyas, sometimes showed Their mercy by killing asuras, but Lord Śrī Caitanya Mahāprabhu awarded love of God without difficulty even to the asuras. All the incarnations of the Supreme Personality of Godhead—but especially Lord Rāmacandra, Lord Kṛṣṇa and, later, Lord Śrī Caitanya Mahāprabhu—delivered many of the living entities present before Them, indeed almost all of them.

Śrī Caitanya Mahāprabhu is therefore represented in the six-armed form of ṣaḍ-bhūja-mūrti, which is a combination of Lord Rāmacandra, Lord Kṛṣṇa and Lord Śrī Caitanya Mahāprabhu. The best purpose of human life can be fulfilled by worshiping the ṣaḍ-bhūja-mūrti, the form of the Lord with six arms—two arms of Rāmacandra, two arms of Kṛṣṇa and two arms of Śrī Caitanya Mahāprabhu.”
(Śrīmad-Bhāgavatam 5.19.8 >> Purport | 1975 Edition)