A polynomial is an expression with coefficients and variables. It can have multiple terms and the exponents of variables can only be positive integers.
In this case, we have two terms, 8x and -2y, both have a coefficient, 8 and 2, and a variabe, x and y, and their exponents are 1, so it is a positive integer.
So, this is a polynomial.
Since it has two terms, it is called a binomial.