Step 1 :Let's find all the zeros of the function \(f(x)=2 x^{3}+7 x^{2}-28 x+12\).
Step 2 :First, we find the roots of the equation by using the coefficients of the polynomial.
Step 3 :The coefficients of the polynomial are [2, 7, -28, 12].
Step 4 :By solving the equation, we find the roots to be [-6.000000000000002, 0.49999999999999983, 2.0].
Step 5 :We then sort the roots in ascending order to get [-6.000000000000002, 0.49999999999999983, 2.0].
Step 6 :The roots of the equation are -6, 0.5, and 2. There are no double roots.
Step 7 :The number in the green box would be the denominator of the fractional root, which is 0.5. Since 0.5 can be expressed as 1/2, the number in the green box is 2.
Step 8 :Final Answer: \(\boxed{2}\).