Can you explain me the meaning of that sentence -- No good. Can you explain the meaning of the sentence to me?-- OK. How can we identify verbs those take second object if its is a prepositional object with to?-- It is a matter of the specific verb. You will have to learn which ones are ditransitive. Start here:
*"Can you explain me the meaning of that sentence" is ungrammatical, but "Can you explain the meaning of the sentence to me" is OK.
There are two syntactic points at issue here. First, the verb "explain" is monotransitive, hence it cannot take two objects, (which explains why your first example is ungrammatical). Second, preposition phrases like "to me" cannot be objects, so although your
BillJ: I thought the verb "explain" was a transitive verb. It is, but it's monotransitive, which means it takes only one object. "To me" is not an object. To identify the verbs that take two objects if we ask a question to the verb e.g.