What is the justification for giving a girl one dirham out of the 600 dirhams left by her deceased father, while she has 12 brothers?

The issue mentioned in the question is incorrect. The least a girl can receive with her brothers is twenty-four dirhams. The correct understanding is that the questioner perhaps intended the case of Ali ibn Abi Talib, in which a woman came to him saying she only received one dinar from her brother's inheritance of five hundred dinars. Ali replied that her brother might have left behind a wife, two daughters, a mother, twelve brothers, and you, and the woman confirmed it. In this case, the wife's share is one-eighth (75 dinars), the two daughters' share is two-thirds (400 dinars), the mother's share is one-sixth (100 dinars), and the remaining (25 dinars) is distributed among the male siblings and the sister, with each male receiving two dinars and the sister receiving one dinar.