It’s hard to know without knowing what is covered in each class in your school, but I wouldn’t recommend skipping it if the normal sequence is beginner algebra --> intermediate algebra --> college algebra, unless you are willing and able to get the curriculum for intermediate algebra and go over the topics yourself to make sure you understand them.
Not knowing how to do the problem initially suggests to me that there are topics in beginner algebra that you do not know, and I would suspect that there are also topics in intermediate algebra that you do now know how to do. It’s great that you pick it up quickly, but if you skip to college algebra, then they would assume you are already comfortable with intermediate algebra and it’s possible you might not know or understand the topics in that subject. It can be hard to do well in a class when they are assuming you have knowledge that you do not actually have. Math is a subject that builds on previous classes, so it’s important to have a good foundation before moving onto the next class.
I agree with audreh–even if you aren’t required to take the placement test, it can be a good idea to take it to get an idea of what level you should be at. If you can, you can also try to get the syllabus and/or old final exams for the intermediate algebra class to see if it’s all stuff you already know or can pick up quickly with a little review.