The Arabic phrase bi-la kayfa, also bi l kaifa, (Arabic: بلا كيف) is roughly translated as "without asking how," or "without [knowing] how". It was a way of resolving theological problems in Islam over apparent contradictions in verses in the Qur'an by accepting without questioning. 
An example is (what some thought was) the contradiction between references to God (Arabic: الله Allāh) having human characteristics (such as the "Hand of God" or the "Face of God"), and the Islamic concept of God as being transcendental, as evident in the Quranic verse "There is nothing like unto Him, and He is the Hearing, the Seeing," (Quran 42:11). Another was the question of how the Quran could be both the word of God, but never have been created by God because (as many Hadith testified) it has always existed. 
Abu al-Hasan al-Ash'ari (ca. 873-936) originated the use of the term in his development of the orthodox Ash'ari school against some of the paradoxes in the rationalist Mu'tazilah school of thought. Instead of explaining that God has a literal face (which would anthropomorphize God) he explained that the earliest Muslims simply accepted the verses as they stand, without asking how or why. This view was held by the vast majority of Sunni Muslims from the first generations of Islam.
In reality both Ibn Hanbal and Abu al-Hasan al-Ash'ari held the same creed of and consisted of accepting the words of the mutashabihat or 'unapparent meanings' of the Qur'an and hadith as they have come without saying how they are meant.
The term "bi-la kayf" is the belief that the verses of the Qur'an with an "unapparent meaning" should be accepted as they have come without saying how they are meant. For example, Imam Ahmad was asked about the hadiths mentioning “Allah’s descending,” “seeing Allah,” and “placing His foot on hell”; and the like, and he replied: “We believe in them and consider them true, without ‘how’ and without ‘meaning’ (bi la kayfa wa la ma‘na).
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- (Quran 42:11)
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- Kawthari, Daf‘ shubah al-tashbih. Cairo n.d. Reprint. Cairo: al-Maktaba al-Tawfiqiyya, 1396/1976, 28