Step 1: Meaning of LMCT energy.
This is the energy to move an electron from oxygen to the metal, and it falls as the metal accepts electrons more easily.
Step 2: Trend down the group.
Going from chromium to molybdenum to tungsten the metal orbitals spread out and sit lower, so the charge transfer needs less energy.
Step 3: Order.
\[ [\text{CrO}_4]^{2-} > [\text{MoO}_4]^{2-} > [\text{WO}_4]^{2-} \]
Step 4: Answer.
\[ \boxed{[\text{CrO}_4]^{2-} > [\text{MoO}_4]^{2-} > [\text{WO}_4]^{2-}} \]