Short answer. Section 6 of Rule 13 provides a fallback: if no one is found at counsel's office, the office is unknown, or there is no office, leave the copy at the party's or counsel's residence (if known) with a person of sufficient age and discretion residing there, between 8 a.m. and 6 p.m.
What the law says
If no person is found in his or her office, or his or her office is not known, or he or she has no office, then by leaving the copy, between the hours of eight in the morning and six in the evening, at the party's or counsel's residence, if known, with a person of sufficient age and discretion residing therein.
Rule 13, Section 6 — Personal [s]ervice. Read the full provision →
The primary method: delivery at the office
Section 6 describes personal service as, first, delivering a copy of the court submission to the party, their counsel, or the counsel's authorized representative named in the relevant pleading or motion. Alternatively, it can be done by leaving the copy at counsel's office with the clerk, or with a person having charge of the office. This is the primary route the section contemplates before any fallback becomes necessary, and it is the method a server should always attempt first.
When the office route fails
Section 6 anticipates that the office-delivery route will not always work: if no person is found in his or her office, or his or her office is not known, or he or she has no office. All three of these are treated the same way — whether nobody is present, the office's location isn't known, or there simply is no office to begin with, the section moves to a fallback method rather than leaving the serving party stuck without any way to complete service on the intended recipient at all.
The residence fallback, with time-of-day and recipient limits
In that situation, service may be done by leaving the copy, between the hours of eight in the morning and six in the evening, at the party's or counsel's residence, if known, with a person of sufficient age and discretion residing therein. This fallback comes with real constraints: it only works if the residence is actually known, it must happen within that specific daytime window, and the person receiving it at the residence must be of sufficient age and discretion — not just anyone who happens to answer the door, such as a young child or a stranger. These limits exist to make sure whoever ultimately receives the pleading is actually capable of passing it along to the intended party or counsel.