Use structural induction on the finite list xs, with the assertion quantified over every accumulator e and every list ys. The equations of the left fold are foldl f e [] = e and foldl f e (x:xs) = foldl f (f e x) xs.
For xs = [], both sides reduce to foldl f e ys. For the constructor case, equational reasoning gives
foldl f e ((x:xs) ++ ys)
= foldl f e (x : (xs ++ ys))
= foldl f (f e x) (xs ++ ys)
= foldl f (foldl f (f e x) xs) ys
= foldl f (foldl f e (x:xs)) ys
The third equality uses the induction hypothesis with accumulator f e x. Hence the stated identity holds. No inspection of ys was required: in Haskell this equality also permits infinite or partially defined ys, with both expressions denoting the same possibly undefined result.
Again use structural induction on the finite list. At [], both the right fold and the left fold return e. For x:xs, use reverse (x:xs) = reverse xs ++ [x], part (a), and the definition of flip:
foldl (flip f) e (reverse (x:xs))
= foldl (flip f) e (reverse xs ++ [x])
= foldl (flip f) (foldl (flip f) e (reverse xs)) [x]
= flip f (foldl (flip f) e (reverse xs)) x
= f x (foldl (flip f) e (reverse xs))
= f x (foldr f e xs)
= foldr f e (x:xs)
The penultimate equality uses the induction hypothesis. Thus foldr f e xs = foldl (flip f) e (reverse xs). Finiteness matters: reversing an infinite list does not produce its first element, whereas some right folds do.
Use the right fold definition xs ++ ys = foldr (:) ys xs, the right-identity law xs ++ [] = xs, and the finite-list involution law reverse (reverse xs) = xs. The last two laws are the additional results used here. Part (b) now gives
xs ++ ys
= foldr (:) ys xs
= foldl (flip (:)) ys (reverse xs)
Set ys = [] to obtain xs = foldl (flip (:)) [] (reverse xs). Substitute reverse xs for xs and simplify the double reversal:
reverse xs
= foldl (flip (:)) [] (reverse (reverse xs))
= foldl (flip (:)) [] xs
The derived Haskell definition is therefore
reverse :: [a] -> [a]
reverse = foldl (flip (:)) []
Each step prepends the next element to the accumulator. This is a left fold derivation from list concatenation, rather than merely a proposed implementation.

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