Well, the Encyclopedia of Hebrew Language and Linguistics calls a verb whose complement is a prepositional phrase, a phrasal verb, but I do not find the definition a transitive verb useful: for me תָּמַךְ בְּ־ isn't a transitive verb, even though in English and other Standard European languages it has a direct object, but if you define phrasal verb simply as verbs which governs a preposition, well, then Brill is right of course. And if I cite this definition of a phrasel verb, the usual one, English speakers use for English: "This semantic unit cannot be understood based upon the meanings of the individual parts, but must be taken as a whole. In other words, the meaning is non-compositional and thus unpredictable", it is wholly absurd to say, that the meaning of the combination of verb and preposition תָּמַךְ בְּ־ is totally unpredicable from its parts. Your support has its force of action at a specific location! But maybe I am too deep into traditional grammar terminology...
Is there a list somewhere to compare the words and an explanation when to use them. There is logic in this, I just don't know this logic yet. Li, sheli, oti, bi all have to do with I and me. Bahem, lahem etc. with them and they. Would be handy to compare and know when to use which one.
And also structural support. I suspect this is the word's origin, hence the usage of "ב-" instead of "את" that confused some of the commentators. One can think of it as an internal strengh, even when in fact it is aid coming from outside.
(On similar note it is also interesting to consider the corelation to the root ס.מ.כ., meaning originally to lean on and developed also the meaning of trust. If something has enough תומכים it can handle more סומכים...)
Well, consult a good dictionary. Or failing this, pay attention how the sentences here are formed and make a mental note that the English transitive verb to support someone or something needs the preposition בְּ־ in Hebrew. Learning at Duolingo means paying attention why your solution was false, and every verb must be treated as an individual.