Arab farmers worked together for social and security reasons, and a single plow was not very effective.
However, the fact that the author mentions twelve pairs rather than simply many is a call to the ancient reader to understand the liturgical significance. Numbers are always significant in the Bible because an "accounting" communicates legal accountability. Hence, Jesus was "numbered with the transgressors" (Isaiah 53:12). This is also the reason the Jewish saints are numbered in Revelation 7 but the Gentile saints are not. The Jews were under the Law and therefore "numbered," so the passage replicates the repetitive nature of the book of Numbers. (Note that the Levites, not "connected" to the Land, were not to be numbered: Numbers 1:49).
What is the "liturgical significance." It is sacrificial. Elijah built a twelve stone altar on Carmel as a sacrificial substitute for Israel. What Elijah did in miniature (a "mountain" covered in blood and washed in water), God did at full size, slaying the priests of Baal and disposing of the bodies in the brook. The twelve stones were a "liturgical model" of Carmel. The heavenly fire upon the sacrifice became the fire of the Spirit in the hearts of God's armed servants.
Elisha's oxen also become a liturgical model of Israel. Since oxen are "servants" they picture priesthood, men who humble themselves before God and serve in His household. As a side note, the four faces of the cherubim correspond to the four compass points of the Tabernacle, with the face of the ox corresponding to the Bronze Altar, and the house of Moses and Aaron. Solomon's bronze sea was carried by twelve oxen, the twelve priestly tribes under the crystal sea (replicating the architecture of Israel under the "sapphire pavement" of Exodus 24). The picture is of Israel bearing the burden of the Law for the nations. Indeed, 70 bulls were sacrificed at the Feast of Booths for the 70 nations listed in Genesis 10.
Elisha's twenty-four oxen are no doubt priestly, so what is the significance of yoking? Yoking has to do with binding in Covenant, as Israel bound herself to false gods in Numbers, replicating the sin of the golden ox. We see the phrase in both the Old and New Testaments:
So Israel yoked himself to Baal of Peor. And the anger of the Lord was kindled against Israel. (Numbers 25:3)
Do not be unequally yoked with unbelievers. For what partnership has righteousness with lawlessness? Or what fellowship has light with darkness? (2 Cor 6:14)
In Numbers, the passage follows the order of the Ten Words, with this "yoking" corresponding to taking the Lord's name in vain. Taking the Lord's name refers to taking the Covenant oath, the "amen" which makes one accountable to God.
So it seems the twelve yoke of oxen are not the tribes in this case but the priests bound by Covenant, most likely a reference to the twenty-four courses of Aaronic priests set up by David (1 Chron. 24:1-19). The flesh is boiled with the yokes and eaten by the people, a reversal of the sacrifices for the people being eaten by the priests and by God. The old priesthood would be utterly consumed and its authority temporarily transfered to God's legal witnesses, the prophets.
So, Elijah calls Elisha from service under the Davidic Covenant to the prophetic ministry given to him on Horeb earlier in the chapter. Elijah was now a new Moses commissioned to deal with Israel's idolatry. He comes down the mountain and "the golden calf" is consumed. In this case, it is the Temple of Solomon.
We see the same ministry in Paul, who is commissioned in the wilderness, then sent to the Gentiles to provoke Israel to jealousy. The legal witness of the prophets brings down fire from heaven (Pentecost) and for those who reject this sign, the eventual destruction of the old house and its priesthood. Aligning these two events it seems that this consumption of the numbered oxen is like the Pentecostal sealing of the 144,000 "numbered" firstfruits Jewish believers in Revelation 7. Their sacrificial "consumption" (martyrdom) seals the guilt of the old order.