Sounds like Veronica is casually putting herself out there and putting the ball in Archie's court. I don't think there is any need for Archie to give his number. If he's interested, he should be polite and give her a call a bit in advance (night before or at least morning of) to say that he'll be in her neighborhood and will be done around X time and wants to know whether she's available for coffee.
Calling with some notice is not only polite, but if Veronica doesn't answer, it then gives him the opportunity to leave a message with his number.
If Archie does indeed like Veronica, I'm sure he can find an excuse to be in her neighborhood or to stop by the office even if he's not really scheduled to work.
Hmm, thanks. This is what I thought, too.
I am Veronica. I gave Archie my number when we were both rushing off in opposite directions, and he didn't give me his back. Heard nothing from him for a week, so thought, oh well. But then I worked with him again and he said, 'Oh, could you give me your number again, I lost it when I had to get a new SIM card on my phone'. At the same time, he wrote his number down and gave it to me.
I was a bit nonplussed. The lost-number thing sounds weird (since I gave it to him on a scrap of paper). And I felt like he was putting the onus back on *me* by giving me
his number, which vaguely rubbed me up the wrong way.
Would you feel the same?

(If I'm overthinking or being unfair, please be honest).