What is the ruling on someone who made a vow not to perform a bad deed, and to fast six days if he were to perform it, then twice intended to do it but did not complete it; and is expiation required of him for that?

This vow falls under the category of a vow of obstinacy (nadhr (definition) al-lajaj), and its maker has the choice between fulfilling what he vowed or offering an expiation for an oath (kaffarat yamin (definition)). If what occurred was merely a thought or intention to perform the mentioned act, and an attempt to begin it without actually entering into it, then there is no breaking of the vow (hinth). However, if he began the act, then he has broken the vow, even if he did not complete it. And if this act is not permissible শরীয়াহ (Islamically), then it is obligatory to refrain from it.