L _ _ D _ _ _ _ _ L _ _ D _ _ _ _ _ L _ _ D _ _ _ _ _ L _ _ D _ _ _ _ _ L _ _ D D _ _ L _ _ _ _ _ D _ _ L _ _ _ _ _ D _ _ L _ _ _ _ _ D _ _ L _ _ _ _ _ D _ _ L For each of those 10 ways above to have exactly 2 letters between the letters L and D, the blanks can be filled with all distinguishable arrangements of the 6 letters CAENAR, which has 2 indistinguishable A's. The number of distinguishable arrangements of CAENAR isSo the final answer is: Edwin