To get beyond rote memorization in a mechanism it is useful to be able to analyze each step in a reaction to decide if it is governed by kinetic or thermodynamic factors or, in some cases, both. Is the product distribution of a process governed by relative transition state energies, relative product stability, or both? The two reactions here highlight these ideas. In the first equation the environment is basic with a large base being employed; this results in the less substituted alkene as the major product. In the second equation the environment is acidic, and the outcome favours the more substituted alkene being the major product.
Using the large reagent potassium t-butoxide, the first reaction medium is basic and somehow this results in the less stable alkene being formed. We can make quick decisions about the mechanism. Firstly, we expect the basic reagent to attack the organic substrate, and basic conditions mean a carbocation is unlikely. Since a large base is used, nucleophilic attack is slowed down and elimination takes over, with the base attacking a beta proton and the bromide being lost, to give the pi bond.
No carbocation means this is likely to be a concerted process. The formation of the less stable alkene suggests that this is irreversible and no equilibrium is established. Formation of the less substituted alkene is rationalized by the large base going after the more accessible proton, to minimize the transition state energy. Transfer of negative charge from very reactive oxygen in the base to the more stable bromine leaving group is unlikely to reverse. This leads to the conclusion that the outcome here is governed by steric factors in competing transition states in an irreversible and concerted pathway.
The second reaction medium is highly acidic, so we know that something is getting protonated and that no strong bases are present. The OH group is a poor leaving group so for it to be lost it must be converted to the reactive oxonium species by protonation. Almost exclusive formation of the more substituted, and therefore more stable, alkene suggests that an equilibrium is involved that would require loss of leaving group to give a carbocation. That species, which is stabilized by the electronic idea of hyperconjugation, could eliminate from either side to give the less substituted and more substituted alkene. Even if the less substituted alkene is formed it can go backwards under acidic conditions and equilibrate to the more substituted product.