睡得着觉 Shuìdezháo jiào 'Can (get to) sleep'
Note how the object of 睡 shuì, 觉 jiào gets split from it by the complement.
外面在放烟花，他竟睡得着觉。 Wàimiàn zài fàng yānhuā, tā jìng shuìdezháo jiào.
‘He could still get to sleep even if there are fireworks outside.’
明天期末考试，他怎么可能睡得着觉？ Míngtiān qímò kǎoshì, tā zěnme kěnéng shuìdezháo jiào?
‘How could he get to sleep when he’ll have final exams tomorrow?’
发生了这么大的事，他依然睡得着觉。 Fāshēngle zhème dà de shì, tā yīrán shuìdezháo jiào.
‘He could still get to sleep even though such a big incident had happened.’
火车上很吵，很难睡得着觉。 Huǒchē shàng hěn chǎo, hěn nán shuìdezháo jiào.
‘It is so noisy on the train that it’s very difficult to get to sleep.’
尽管很担忧，她也还是睡得着觉。 Jìn’guǎn hěn dānyōu, tā yě hái shì shuìdezháo jiào.
‘Although she is very worried, she still fell asleep.’
Note that 担忧 dānyōu requires no object, but 担心 dānxīn usually needs an one.
睡不着觉 Shuìbuzháo jiào 'Can't (get to) sleep'
听到这个好消息，我兴奋得睡不着觉。 Tīngdào zhège hǎo xiāoxi, wǒ xīngfèn de shuìbuzháo jiào.
‘After hearing this good news, I was too excited to go to sleep.’
我兴奋得睡不着觉。 Wǒ xìngfèn de shuìbuzháo jiào.
‘I’m too excited to sleep.’
明天要去英国，他激动得睡不着觉。 Míngtiān yào qù Yīngguó, tā jīdòngde shuìbuzháo jiào.
‘He will go to the UK tomorrow, and is so excited he can’t sleep.’
听说他住院了，她担心得睡不着觉。 Tīngshuō tā zhùyuànle, tā dānxīn de shuìbuzháo jiào.
‘She heard that he is in hospital; she is too worried to sleep.’
看了恐怖片，她怕得睡不着觉。 Kàn le kǒngbùpiàn, tā pà de shuìbuzháo jiào.
‘After watching a horror film, she is so scared she can’t sleep.’
明天要演讲，他紧张得睡不着觉。 Míngtiān yào yánjiǎng, tā jǐnzhāng de shuìbuzháo jiào.
‘He will make a speech tomorrow, so he is too anxious to sleep.’