Phoenix...everybody takes care of their
plants in the same, yet different ways. A young rosemary
plant is better able to adapt to the way you will take care of it than an older one that's been taken care of by someone else. Repot the 4inch rosemary into a 6inch pot with a good potting mix that drains well. Don't use one with fertilizer mixed in though. Water it in well. Then do not water again until the soil surface is dry 1/2 inch below the surface. Use your finger to test for dryness. Then water the pot well, a little at the time, to the point where water drains from the hole is enough, then let it dry down again. Starting with a small
plant, you won't be watering that much in the beginning. As your
plant gets older, its watering needs will increase. Let your finger always be the determining factor in deciding when to water until you get comfortable with the whole process.
One more thing, do you know the name of the rosemarys you've killed in the past? Here in New Orleans, the variety "Logee's Blue" does really well. oTHER varieties are a little harder, even the ones promoted as heat and humidity tolerant like Athens Blue, developed in Georgia and just sulked its first summer in New Orleans. Folks at a garden center could likely tell you which variety would do best in your area. It all makes a difference. Don't forget lots of sunshine too.