> 1. a numerical or constant quantity placed before and multiplying the variable in an algebraic expression (e.g. 4 in 4x^(y)).
This is Google’s definition of the word, so it’s not necessarily the most accurate thing in the world mathematically, but it is definitely *at least* the level of understanding you need to have. In 2*8x^(2), the 2 cannot be a coefficient because 8x^(2) is not the kind of object that can have a coefficient. The coefficient is the number (16) next to the variable (x^(2)).
Also, if you’re trying to think about what it means, it probably doesn’t help to say “the coefficient of the first term”. 4x^2 + 6x and 6x + 4x^2 are obviously the same so is “the coefficient of the first term” 4 or 6? You can instead say that 4 is the coefficient of x^(2), etc.