Explanation

x=2+2^(1/2)+2^(3/2)=2+3*sqrt(2) gives x^2-4x-2=12, which is not among the options (0, 1, 4, 6) - the stem as stored appears corrupted (likely a wrong exponent). Both the stored key and the published coaching key say C (4), but no consistent working from the given stem yields any listed option, so the stored key is kept. Note: key disputed - independent verification inconclusive.