To multiply the polynomials, we use the distributive property. In this case, we have the polynomial -2y^5 multiplied by the expression (6y - y^2).
To distribute -2y^5 to each term inside the parentheses, we multiply -2y^5 by 6y and -2y^5 by -y^2 separately.
When we multiply -2y^5 by 6y, we multiply the coefficients (-2 and 6) to get -12. Then, we add the exponents of y (5 and 1) to get y^6. Therefore, -2y^5 * 6y = -12y^6.
When we multiply -2y^5 by -y^2, we multiply the coefficients (-2 and -1) to get 2. Then, we add the exponents of y (5 and 2) to get y^7. Therefore, -2y^5 * -y^2 = 2y^7.
Finally, we combine the two terms: -12y^6 + 2y^7. This is the result of multiplying the polynomials -2y^5 and (6y - y^2).