Determine the different possibilities for the numbers of positive, negative, and nonreal complex zeros for the following function. \[ f(x)=2 x^{3}-8 x^{2}+2 x+4 \] What is the possible number of positive real zeros of this function?

Step 1 ：Determine the different possibilities for the numbers of positive, negative, and nonreal complex zeros for the function \(f(x)=2 x^{3}-8 x^{2}+2 x+4\).

Step 2 ：To find the possible number of positive real zeros of a polynomial, we can use Descartes' Rule of Signs. This rule states that the number of positive real zeros of a polynomial is equal to the number of sign changes in the list of its coefficients, or less than that by an even number.

Step 3 ：The coefficients of the polynomial are 2, -8, 2, and 4. The signs of these coefficients are positive, negative, positive, and positive, respectively. Therefore, there are 2 sign changes in the list of coefficients.

Step 4 ：So, the possible number of positive real zeros of this function is 2 or 0.

Step 5 ：Final Answer: The possible number of positive real zeros of the function \(f(x)=2 x^{3}-8 x^{2}+2 x+4\) is \(\boxed{2}\) or \(\boxed{0}\).