Question
Question: Find all possible Lactones with six membered ring having molecular formula $(C_6H_{10}O_2)$, which w...
Find all possible Lactones with six membered ring having molecular formula (C6H10O2), which when reacts with (1) LiAlH4 (2) H2O gives meso diol.

The possible lactones are 3-methyl-6-oxotetrahydro-2H-pyran, 4-methyl-6-oxotetrahydro-2H-pyran, and 5-methyl-6-oxotetrahydro-2H-pyran.
Solution
The problem asks for six-membered ring lactones with formula C6H10O2 that yield a meso diol upon reduction with LiAlH4. Six-membered ring lactones are δ-lactones. With 6 carbon atoms, the lactone is a methyl-substituted δ-pentanolactone. Reduction of a δ-lactone gives a 1,5-diol. The resulting diol is a methyl-substituted hexane-1,5-diol. For the diol to be meso, it must have a plane of symmetry and chiral centers. The possible positions for the methyl group on the hexane-1,5-diol chain (numbering from the primary alcohol) that result in a meso diol are positions 2, 3, and 4, leading to 2-methylhexane-1,5-diol, 3-methylhexane-1,5-diol, and 4-methylhexane-1,5-diol, respectively. These diols have two chiral centers and can exist in meso forms. The corresponding lactones are 3-methyl-6-oxotetrahydro-2H-pyran, 4-methyl-6-oxotetrahydro-2H-pyran, and 5-methyl-6-oxotetrahydro-2H-pyran.