Answer
See table.
Work Step by Step
Step 1. Given $f(x)=2x^5-7x^3+6x+8$, we can identify 2 sign changes indicating that there could be 2 or 0 positive zeros. Put the numbers in the table.
Step 2. $f(-x)=-2x^5+7x^3-6x+8$, we can identify 3 sign changes indicating that there could be 3 or 1 negative zeros. Put the numbers in the table.
Step 3. There should be 4 total zeros. thus the number of nonreal zeros will be the remaining after taking real zeros into account. Complete the table as shown.