What is the coefficient(s) in this equation?

If the answer is "3" then what the heck is the question. If it's "how many coeffients are there?" then the answer is 3, but you never wrote that as a question.

The three coefficients of m^2 - 4m^4 + (7+r) are 1, -4, and (7+r). The last is the coefficient of x^0. I presume r is some constant, not another variable.

Some might argue that the constant is not a coefficient, and if that's the way your teacher wants to treat it, go with it. But if "3" is the answer, that doesn't appear to be the case. Whether it's a "coefficient" or not rarely makes any mathematical difference -- it's just semantics, not really math. Not to downplay the importance of precise definitions of important terms, but "coefficient" generally isn't a critical term.

We usually ignore coefficients of 0, since those terms are simply "missing" from the polynomial. Otherwise what about 0x^1000 and 0x^999 etc.

This is easy. okay the coefficients in this equation are 2, 4, and 4. The constant in this equation is 2, 4, 7, and 4. ( Remember that the constant is all the numbers in the equation )

( Also remember that the coefficient is the numbers next to the variables )