Hi! Just looking for some insight on these problems.
For the first one, I'm pretty much stumped.
What I had is the BF3 behaving like a hydrogen to epoxide and "protonating" the oxygen. Then, given that there is nothing substituted, I assumed it would be something like an Sn1-like reaction (with the partially charged "carbocation"). Then the ring breaks, with the electrons on the left C-O bond going to the now-positively charged Carbon (due to the epoxide breaking) and an C-O-BF3 bond. Then I have elimination occurring with one of the rightmost hydrogens, kicking off the BF3 and creating the carbonyl.
I'm still not quite sure if this is right, especially the portion near the end.
And for the second one, my idea is to brominate the starting material using radical halogenation, then create a Grignard reagent out of that and attack a benzene to add the Ph. However, this is where I'm a bit suspicious - I remember learning that certain electron-withdrawing groups interfere with Grignard reagents (like carbonyls and the like). Though, if that worked, then I would brominate the cyclohexanol-Ph product again (and it would attack at the C-Ph area since it is tertiary) and set up intramolecular epoxide formation. Though I'm still stuck on the Grignard reactivity when influenced by functional groups.
And that's all I have. Thanks for your aid!