You would use suggest to give ideas. like " I suggest checking out the new Volkswagen, they have better quality." Or, "Where do you suggest we go to dinner?" Explain, by definition, is to make something clear to somebody. So by saying "explain me" you are saying "define me". Buy by saying "explain to me" you are telling the person that you need more information about whatever the subject is. Like, "I don't understand how to use this new phone, explain it to me." or, "Can you explain to me, how to get to the closest gas station?"

Part 2 of 2. I can prove my theory by concocting some counter examples. Don't let them confuse you, the rules are valid. By proving that I can create exceptions, I can convince myself that I understand the reason for the rule. We _can_ say "suggest me." Consider this conservation. "Blinktronics just hired me as an electronic engineer. They also need a software engineer and asked me if I could suggest anyone." "Oh, please, suggest me to Blinktronics as a candidate." And we _can_ say "explain me" if we are creative enough. "The origin of things remains a mystery. Perhaps the cosmologists can explain the galaxy, but they cannot explain me." Finally, there is a classic counterexample, although it is a kind of language joke, in "Alice's Adventures in Wonderland." It is joking about two idiomatic usages, "explain yourself" and "I'm not myself." `What do you mean by that?' said the Caterpillar sternly. `Explain yourself!' `I can't explain MYSELF, I'm afraid, sir' said Alice, `because I'm not myself, you see.'

Part 1 of 2. This is an interesting question! I'm going to answer it as a native speaker who understands grammar mostly by intuition. "Please give the book to me" is correct. "Please give me the book" is correct. "Please tell the answer to me" is correct. "Please tell me the answer" is correct. So, why is "Please suggest a good book to me" correct, but "Please suggest me a good book" incorrect? Why is "Please explain the idea to me" correct, but "Please explain me the idea" incorrect? It has to do with the actual meanings of the words "suggest" and "explain." For whatever reason, when we use the word order verb, indirect object, direct object, we do not use the word "to." The sentence structure is simply "Verb personal-pronoun-X Y" and you cannot actually determine which is the direct object and which is the indirect object. "Verb X Y" can only be understood if the actual _meanings_ of the words only allow one interpretation. When X is a person, often it is impossible that X could be the direct object, and when we hear "Verb X ..." we already feel X as the indirect object before we know what is coming. In the rare cases where the meaning of the verb makes it possible for X to be the direct object, then we hear "Verb X ...", feel X as direct object, then hear Y, realize that it is more likely that X is the indirect object. The switch in feeling makes us uncomfortable so we avoid that combination of words.