The minivan in front of us blew a tire and pulled over, a long way away from mobile signal. We couldn't find a spare tire. I have a Technician license; if I'd had my Baofeng BF-F9 V2 with me, is there a way I could have used it to help that family out?
If there's no mobile phone coverage, it's likely there are also no repeaters in range of the Baofeng. You could try the conventional simplex calling frequencies of 146.52 MHz (2m) and 446 MHz (70 cm) to see if someone nearby can help.
A blown tire isn't an emergency, so there's no particular protocol to follow. Simply, "This is [your call], I'm with a motorist in need of a spare tire at [describe location], can anyone assist?" would suffice.
Range with a handheld UHF/VHF radio isn't great, maybe on the order of 10 km in flat terrain. If being out of mobile phone coverage also means you're in the middle of nowhere with few people around, it's unlikely there's someone in range, that's a ham, that's monitoring the calling frequencies, and willing and able to help beyond what you could personally do for the stranded motorist. Practically speaking, offering a ride to the nearest town may be more helpful.
Because the situation does not rise to the level of "imminent threat to life or property" you would not be permitted to "use any means neccessary" to carry out your communications. As a result, you would need to pass your traffic using simplex or an available repeater on ham radio frequency allocations if you are under US jurisdiction at the time. A simple "request for assistance for a stranded motorist" would be sufficient.
The Baofeng BF-F9 is an 8-watt UHF/VHF handytalky. With those frequencies you only have line of sight (a few miles) with the stock antenna, and maybe a little better (20-40 miles) if you were to string up a J-pole antenna up a tree. If you were to climb a mountain, you might be able to hit a more distant repeater.
In other words, it’s not going to do you a whole much but it’s better than nothing. An emergency j-pole is certainly something to consider having in your go bag.