The word "of" is in italics in the original. The phrase you highlighted, more properly formatted as
- "with of before the thing communicated",
means that the word "advise" is accompanied by the word "of", where the word "of" is written "before the thing communicated".
Their example makes this clear:
We were advised of the risk.
The word "of" accompanies the word "advise(d)", and is written before the phrase "the risk" (which is the thing communicated or advised).
As @R.M. comments, this is a 'use-mention distinction':
The distinction between use and mention can be illustrated for the word cheese:
- Use: Cheese is derived from milk.
- Mention: 'Cheese' is derived from the Old English word ċēse.
The first sentence is a statement about the substance called "cheese"; it uses the word 'cheese' to refer to that substance. The second is a statement about the word 'cheese' as a signifier; it mentions the word without using it to refer to anything other than itself.
In the terminology of this distinction, the word "of" in your example is mentioned but not used.