The condition is assumed to be basic. This is basically a reverse of the aldol condensation reaction. We begin with a molecule of (2E)-5-methyl-4-oxohex-2-enoate $(1)$, which undergoes nucleophilic conjugate addition with hydroxide ion ($\ce{OH-}$) acting as nucleophile to produce 2-hydroxy-5...

The condition is assumed to be basic. This is basically a reverse of the aldol condensation reaction. We begin with a molecule of (2E)-5-methyl-4-oxohex-2-enoate $(1)$, which undergoes nucleophilic conjugate addition with hydroxide ion ($\ce{OH-}$) acting as nucleophile to produce 2-hydroxy-5...

What I usually do when I start numbering is look for branching and start numbering at the end with the closest branch. Also, keep in mind that with branching you'll want to consider numbering from one of the branches (if it'll yield a long chain.) I'm using the structure you made as an example:...

Why is Cu(acac)$_{2}$ square planar, whereas Al(acac)$_{3}$ and Fe(acac)$_{3}$ form octahedral complexes? I see how a similar argument to Pt complexes would apply, i.e. with $d^{9}$, there is only one electron that goes in the very destabilised $2b_{1g}$ (corresp. to $d_{x^2-y^2}$) in the square-...