The mechanical energy in this case is the sum of the kinetic energy (KE) and the potential energy (PE). Below are the equations used for solving as well as the substitution.
KE = 0.5mv² = 0.5(2 kg)(1 m/s)² = 1 kg m²/s² = 1 J
PE = mgh = (2 kg)(9.8 m/s²)(0.5 m) = 9.8 kg m²/s² = 9.8 J
The sum of the two energies is the mechanical energy,
ME = KE + PE = 1 J + 9.8 J = 10.8 J
Therefore, the answer is the second choice.