Both honor and dishonor are cause for worry.
Misfortune is caused by the self.
What does it mean to say that honor and dishonor are cause for worry?
The concept of honor is depressing:
You are worried about obtaining it.
Once you have it, you are worried about losing it.
That's why it is said that honor and dishonor are both cause for worry.
What does it mean to say that misfortune is caused by the self?
As long as you are attached to your self, you will suffer.
Without a self, what is there for suffering to affect?
One who regards his responsibilities as his self, however, can be trusted with anything.
One who loves the world as his self can be trusted with caring for it.
This is a very difficult passage to translate, especially since one of the characters is different between two different versions of the Tao Te Ching, the Wang Pi and the Ho Shang Kung (HSK). The fourth line, in Chinese, is only three characters long, glossed like this: [honor makes low]. That's in the Wang Pi version of the TTC, though. Another version, the HSK, has [dishonor makes low]. This is a very difficult situation because the two words used are opposites. Often, the cause of a discrepancy between two of the versions is that somewhere along the way, a scribe mistakenly copied a character as a similar-looking character. In that case, the mistake is easy to spot because in one of the versions, the character has a meaning that seems totally out of place.
Here, though, the two characters don't look anything alike, and so it's likely that what happened was a failure of memory. The copyist remembered the basic gist of the passage, but couldn't remember whether the word in question was honor or dishonor. How could they make such a mistake? Looking at the passage, it's clear; substituting "dishonor" doesn't actually change the meaning very much. In both cases, the passage is saying that attaining honor is stressful, and that getting dishonored is also stressful. However, due to the context I think "honor" is a more likely choice.