You will see the Mark as Solved button only on replies to a topic you started. For example, you should see one on this post, because this post is in reply to the topic "Mark as Solved Button" that you started.
I hope this answers your question.
Clicking the "Kudos star" to the left is a great way to say thanks!
When your problem has been solved, accept the solution by clicking the "Accept as Solution" button to help other members in the future!