Vishnu Purana(4.11.4) says:
यदोर्वंशं नरः श्रुत्वा सर्वपापैः प्रमुच्यते । यत्रावतीर्णं
कृष्णाख्यंपरं ब्रह्मनराकृति ||
yador vaṁśaṁ naraḥ śrutvā sarva-pāpaiḥ pramucyate | yatrāvatīrṇaṁ
kṛṣṇākhyaṁ paraṁ brahma narākṛti ||
Hearing of the dynasty of Yadu, one becomes free of all sins. In that
dynasty appeared Kṛṣṇa, the supreme Brahman in human form.
Bhagavata Purana(7.15.75) says:
यूयं नृलोके बत भूरिभागा लोकं पुनाना मुनयोऽभियन्ति येषां गृहानावसतीति
साक्षाद्गूढं परं ब्रह्म मनुष्यलिङ्गम्
yūyaṁ nṛ-loke bata bhūri-bhāgā lokaṁ punānā munayo ’bhiyanti yeṣāṁ
gṛhān āvasatīti sākṣād gūḍhaṁ paraṁ brahma manuṣya-liṅgam
You Pāṇḍavas are most fortunate in this world. Sages who purify the
planets come to your houses because the Supreme Brahman personally
resides in your houses in a human form.
Arjuna requests Krishna to show four handed form:
tenaiva rūpeṇa catur-bhujena sahasra-bāho bhava viśva-mūrte ||
O thousand-armed one, form of the universe! Appear with that
four-armed form. BG 11.46
After showing four handed form, Krishna takes his two handed form again.
dṛṣṭvedaṁ mānuṣaṁ rūpaṁ tava saumyaṁ janārdana | idānīm asmi saṁvṛttaḥ
sa-cetāḥ prakṛtiṁ gataḥ ||
O Janārdana, seeing your pleasant human form, my mind has become
peaceful and I have gained composure. BG 11.51
Vishnu Sahasranama of Padma Purana(6.71.249) says:
नराकृतिः परंब्रह्म narākrṭi param brahma
[Kṛṣṇa is] the supreme
Brahman in human form.
From all these, we can conclude that Krishna moved around in 2 handed form.
At few places, he showed four handed forms.
While taking birth, Krishna appeared in four handed form:
Bhagavata Purana(10.3.9-10) says:
tam adbhutaṁ bālakam ambujekṣaṇaṁ catur-bhujaṁ śaṅkha-gadāry-udāyudham
| śrīvatsa-lakṣmaṁ gala-śobhi-kaustubhaṁ pītāmbaraṁ
sāndra-payoda-saubhagam || mahārha-vaidūrya-kirīṭa-kuṇḍalatviṣā
pariṣvakta-sahasra-kuntalam | uddāma-kāñcy-aṅgada-kaṅkaṇādibhir
virocamānaṁ vasudeva aikṣata ||
Vasudeva saw an amazing boy: His eyes resembled two lotuses. His four
arms held eminent weapons: the conch, the mace and the cakra. He had
the mark of Śrīvatsa. On His neck, the Kaustubha was dazzling. His
garments were yellow. His splendor was more charming than the hue of
rain clouds. His immeasurable head hair mingled with the effulgence of
His two earrings and of His crown, which was studded with the highly
valuable Vaidūrya gem. And He was especially resplendent with His
magnificent girdle, armlets, and forearm ornaments.
The reason why Krishna appeared in 4 handed form instead of 2 handed form directly is explained in the same chapter later.
Bhagavata Purana(10.3.44) says:
etad vāṁ darśitaṁ rūpaṁ prāg-janma-smaraṇāya me | nānyathā mad-bhavaṁ
jñānaṁ martya-liṅgena jāyate ||
This form is shown to both of you for the sake of reminding you about
My past lives, otherwise knowledge of Me does not occur, because I
have a characteristic of mortals.[The sense is: because I am Para-Brahman in a
Another instance where Krishna manifested four arms:
Bhagavata Purana(10.60.26) says:
paryaṅkād avaruhyāśu tām utthāpya catur-bhujaḥ keśān samuhya
tad-vaktraṁ prāmṛjat padma-pāṇinā
The Lord quickly got down from the bed. Manifesting four arms, He
picked her up, gathered her hair and caressed her face with His lotus
Vishwanath Chakravarty Thakur comments that Lord manifested four arms to do these activities simultaneously.
Another instance where Krishna manifested four hands:
Bhagavata Purana(1.7.52) says:
niśamya bhīma-gaditaṁ draupadyāś ca catur-bhujaḥ ālokya vadanaṁ
sakhyur idam āha hasann iva
Hearing the words of Bhima and Draupadi, Krsna with four hands looked
towards his friend Arjuna while smiling and spoke.
The reason why Krishna manifested 4 arms here is explained by Sridhara Svami and Vishwanath Chakravarty as follows.
Bhima favored killing Asvatthama and Draupadi favored releasing him. The
Lord assumed four arms to keep the two parties apart.