I'm a Japanese speaker and noticed that this phrase sounds similar to しつれいします (shitsurei -shimasu) in Japanese which means roughly the same thing as 실례합니다 . Sure enough, both derive from the Chinese word, 失禮 (shi 1 li 3) meaning that one has made an etiquette mistake. Cool.
시-ㄹ-에-합-니-다 (shil-ae-ham-ni-da) if you break it down like this it may help. It's not the right spelling but I hope it helps! I wouldn't rely on direct translations like romanji, it kinda makes you emphisise on words that shouldn't be emphasized on, so just focus on learning the characters for now
를 is aㅜ object marker, and is the same as 을, they are used depending on if it follows a consonant or a vowel e.g. 한국어를 배웠어 Korean (is the object of) learn (in the past tense) = I learnt Korean 이름을 배웠어 Name (is the object of) learn (in the past tense) = I learnt the name
However, for simple sentences and casual setting, usually you emit the object marker and just say "한국어 배웠어", but they are used in formal contexts like a written paper, or respecting elders (maybe?), and definitely for more complex sentence structures, so people know which subject corresponds to which verb. Or you can use it to emphasize the subject like: 한국어를!~ 배웠어! = KOREAN! I learnt it!
I am not a native speaker, this is just my understanding, so please correct me if im wrong! (: 감사합니다~