To me, the main bits of context that helps you understand this word are "business," "contacted" and "clients." Because of these three words, you can have an idea as to what is going on.
If Brad is contacting clients, we know that he is getting in touch with them. We also know that Michelle is doing something similar. We know this because the sentence is contrasting the two of them. Brad is doing this by phone, Michelle is doing it door to door.
We know that Michelle is doing this as a way to get business. That ties in with the word "clients." So we know that Michelle is contacting potential clients to get their business. That tells us pretty much the whole definition of "solicit."
The phrase "by going door to door" implies the sense that a person is asking for something or selling something, both of which can be related to the meaning of the word "solicited." Also, the word "business" which is the object of the verb "solicited" indicates that Michelle is seeking out business, or asking for business. The only other reason for going door-to-door would be to do a survey, which does not reflect asking for money or asking for business, but in this case, the person COULD be soliciting information - in any case, it is asking for something.
In the second part of the sentence, the clause "while Brad contacted clients over the phone" also implies that something is being sold or asked for. First of all, Brad is contacting people and the people are clients. Clients are those with whom one has a business relationship and if Brad is contacting them, the meaning implied is that he is "asking for business" or "soliciting business".