Dr. Gomez, a veterinarian, noticed that she only had about 12 ounces of cat treats left. So, she bought a new 3-pound jar. If she uses about 6 ounces of cat treats every week, in how many weeks will she run out?

Since 1 pound is equal to 16 ounces, then the 3-pound jar of cat treats is equal to 3 x 16 = <<3*16=48>>48 ounces.

Dr. Gomez has a total of 48 + 12 = <<48+12=60>>60 ounces of cat treats.
Therefore, she can use the cat treats for 60/6 = <<60/6=10>>10 weeks. Answer: \boxed{10}.

To answer this question, we can follow these steps:

Step 1: Convert the new jar capacity from pounds to ounces.
1 pound = 16 ounces.
So, a 3-pound jar would be 3 x 16 = 48 ounces.

Step 2: Calculate the total amount of cat treats available by adding the remaining treats with the jar's capacity.
Remaining treats = 12 ounces.
Total treats = Remaining treats + Jar capacity = 12 + 48 = 60 ounces.

Step 3: Divide the total treats by the weekly consumption to determine the number of weeks to run out.
Weekly consumption = 6 ounces.
Number of weeks = Total treats / Weekly consumption = 60 / 6 = 10.

Therefore, Dr. Gomez will run out of cat treats in 10 weeks.