Final answer:
The problem is a linear nonhomogeneous differential equation typically solved through methods like undetermined coefficients, but the provided information is unrelated and cannot be used to solve it.
Step-by-step explanation:
The differential equation y"+2y'-24y=16-(x+2)e^4x falls under the subject of Mathematics, and it is generally studied at the college level, although advanced high school students may also encounter this type of problem.
To solve this differential equation, we would typically use methods for solving linear nonhomogeneous differential equations, such as the method of undetermined coefficients or variation of parameters. However, the provided information seems unrelated to the differential equation at hand and could not be used to solve it.