Each blank here is supported by several clues, so start with whichever one you feel more comfortable with. The first blank says something about recipes for beef brisket. The opening clause of the sentence indicates that these recipes "vary widely," and the detour road sign "but" means the blank will be the opposite of that—a word to indicate what they have in common. Similarity would be a good prediction. (A) affinity, or "close resemblance," is a perfect match, so it's the right answer for the first blank. (B) variance means "difference," so it's the opposite of what you're looking for. (C) substitution might be tempting because it's a word often used in cooking; if you're out of one ingredient, you'd substitute another. However, it doesn't fit the context here, since the sentence is describing a technique different preparations share, not one that replaces another.

The second blank describes why the "low and slow" technique is used. The first clause says that it's "not a matter of taste but ... ," a detour construction, so the missing word must contrast with the idea that the cooking method is simply a personal preference. After a semicolon, which functions as a straight-ahead road sign here, the sentence indicates that without this method, the meat would be "too tough" to eat. Since cooking food in a way that makes it inedible defeats the purpose, predict something like necessity. (D) prerequisite, or "something that is necessary," matches this prediction, so it's the correct answer. (E) predilection means "a liking for," which would fit if the cooking method were just a matter of taste. (F) propinquity, which means "a closeness or similarity to," does not fit the context.