The major difference between analytical and synthetic thinking is the type of an approach. While analytical thinking takes an outside perspective moving from something big to its smaller parts, synthetic thinking takes the inside perspective. It means that if there are many separate ideas flowing in the space, using the approach of synthetic thinking you can create one big one moving step-by-step to it. This is a more creative approach because it lets you come up with new forms of the well-known concepts.
If we compare the analytical statements with synthetic ones, we will see a huge difference. The latter ones are not obvious. We can't use the definitions from the dictionary to prove that a statement is right or wrong. That is when the creativity plays its significant part. If you want to improve your synthetic thinking skills, you can get engaged in a creative activity, have a new hobby, start solving non-trivial puzzles. All of these things will help you train your brain better. Try to notice something that is not obvious as you might be the only one to notice it. That is the perfect way to stand out from the rest.