Subordination in English is one of the more complex areas of the grammar, and I didn't study this until my honours year. That anyone ever gets is is amazing.
Suggest (this particular version anyway) takes a full S (sentence) as a complement, subordinated by an optional that. So in effect, when you see a sentence with suggest in it, you should be able to remove everything up to suggest(s) (that), and the result should be complete, and grammatical.
My father suggested that I subscribe to Newsweek.
In the above, I subscribe to Newsweek is a fully complete, grammatical sentence.
Encourage works differently. It does not take a complete S as its complement; it takes what Lexical-Functional Grammar calls an XCOMP, which is essentially a non-finite verb phrase. As it's a verb phrase, it lacks an agent (ordinarily mapped to subject), which it must absorb from the matrix clause, and it lacks tense inflection, which it inherits from the matrix clause.
Consider the following:
I subscribe to Newsweek.
I is the agent, and Newsweek is the, well, patient (not exactly, but it'll do). Agent maps to subject, patient maps to object. Easy.
He encouraged [ me to subscribe to Newsweek ]
Here, me is the agent of subscribe, but it comes out as me rather than I, the accusative form. What's happening here is that the matrix clause he encouraged me supplies its object, me, to the subordinated clause to act as the agent of the verb subscribe.
To make matters worse, there are intransitive verbs that take an XCOMP as well, but in those scenarios, there's no object of the matrix clause to act as the agent of the subordinate clause, so instead it uses the subject of the matrix clause:
I promise to do the dishes.
It is I that does the dishes, which that clause gets from the matrix clause.
So to sum, B is correct. D would have been correct if it had been encouraged me to.
Which verbs work like suggest and which like encourage is just something that you have to learn; there's no pattern to it, it's simply arbitrary.