Will my car make this roadtrip?

I have a 2004 Ford Focus with 164,000 miles. Everything runs well. I want to take a trip to Santa Barbara which is 6 hours away from where I live, but my dad tells me I shouldn't take it because it could break down. Is that true? He says I shouldn't even drive it two hours to phoenix…

It's automatic and a 4 cylinder

A lot of this depends on how well its been maintained. Have a professional mechanic check it out.

If it's been well maintained, has good oil and coolant, transmission oil, four good tyres and you drive it sympathetically there's no reason why it shouldn't make it.
If you drive it all the way with the rev counter just below the red there's a chance you'll blow it, But run at 3000 to3500 rpm and it should go all day

You should have no issues with a well cared for vehicle… There are things that can happen to any car with higher mileage. Timing belt being the most serious.