Let’s talk about question marks for a little bit. (Okay, more accurately I’ll write and you can read.)

I’ll bet you learned in school that you put a question mark at the end of an interrogative sentence. Take a look at the title of this post. Is that really a question? Is it asking a question?

It isn’t. It’s making a statement about the subject (he) wondering something (if he was right). There’s no question mark at the end of a declarative sentence like that one. (Or this one that I just wrote.)

Was he right, he wondered?

Now there you can use a question mark, because it’s phrased as a question (“was he right?”). Stylistically, the tag “he wondered” can be considered part of the question if you like the look of it because this is indirect speech/thought. Alternatively, you might have

Was he right? he wondered.

which is another stylistic option, as is

Was he right? he wondered. (with italics for the thought, presented indirectly instead of Am I right? he wondered.)

All of those are acceptable. The way it’s written in the title of this post, however, is not.