This is the 1719th most frequent Arabic word.
لكنهم
"But they" or "But they are."
The word "لكنهم" is used as a conjunction (but) here to show contrast between the clause before it (their attempt to finish quickly) and the clause after it (not being able to finish due to obstacles). It also includes the pronoun "هم" (they), linking the contrast directly to a specific subject.
حاولوا أن ينهوا العمل بسرعة، لكنهم لم يتمكنوا بسبب العقبات.
They tried to finish the work quickly, but they couldn't due to obstacles.
In this sentence, "لكنهم" is again used as a conjunction (but), creating a contrast between the desire of the children to play outside and their actual action of staying inside. The pronoun "هم" links the contrast to the children as subjects.
الأطفال أرادوا اللعب في الخارج، لكنهم بقوا في الداخل بسبب المطر.
The children wanted to play outside, but they stayed inside because of the rain.
Here, "لكنهم" contrasts the expectation (thinking they would attend) with the reality (their decision not to attend). The pronoun "هم" identifies whom the contrast refers to.