To intuit something is to know it, or to make a good guess, from a feeling — not from facts you can point to and line up. You cannot always say how you know; you just do. It is a fairly formal or educated verb; in everyday speech people more often say I just had a feeling, I could tell, or I sensed it. You might intuit that a friend is upset from their face, or intuit the answer before you work it out on paper. Though actually, the word does not claim magic: teachers sometimes note that “intuition” is often the brain using small clues very fast. Still, intuit itself only says you did not reason it out step by step. You intuit that… or intuit something; you do not usually “intuit about.”