1. Explain it simply
尽管 (jǐnguǎn) means 'even though'; it concedes a fact that is truly the case.
Word order: 尽管 + fact + comma + 但是 / 可是 + result.
The second clause often adds 还是 or 还 to stress that the result holds anyway.
尽管 stays at the head of the first clause and 但是 at the head of the second - never stack them together or swap them.
2. Show examples
尽管天气很冷，但是他还是去跑步。
Jǐnguǎn tiānqì hěn lěng, dànshì tā háishì qù pǎobù.
Even though the weather is cold, he still goes running.
尽管 concedes, 但是 turns
尽管他很累，可是他还在工作。
Jǐnguǎn tā hěn lèi, kěshì tā hái zài gōngzuò.
Even though he's tired, he's still working.
可是 works the same as 但是
尽管他很努力，但是成绩还是不太好。
Jǐnguǎn tā hěn nǔlì, dànshì chéngjì háishì bù tài hǎo.
Sandhi:Jǐnguǎn tā hěn nǔlì, dànshì chéngjì háishì bú tài hǎo.
Even though he works hard, his grades still aren't very good.
keep 尽管 and 但是 in separate clauses
3. Share a tip
尽管 is not 不管 - 尽管 grants a fact, so pair it with 但是, not with a choice like 不管 A 还是 B.