I want to know, what would be best delay time to change slides in carousel.
As Evil Closet Monkey astutely points out in the comments, your goals probably won't be answered by a carousel. In fact, the time-delayed slider solves almost zero real business needs.
Think of it this way: The content is either worth putting on the page or not.
If you must
Anything after the first slide might as well not be there. Chances are, every slide after the first is just there to appease someone's misguided agenda.
Carousels are effective at being able to tell people in Marketing/Senior Management that their latest idea is on the Home Page. —Lee Duddell
So design around that problem. Set the delay to the maximum duration you can get away with before the executive in question complains. 5-6 seconds should do. Then your users never have to be bothered by it but executives feel validated.
On the off chance that the additional content has some value, include paging controls. This gives the rare curious user who has the patience to look around the chance to see more content exactly when they want it. Once a user manually controls the slideshow, turn off the auto-play script.
The carousel is made to draw the user's attention to something important.
When the carousel rotates too quickly users don’t have enough time to investigate interesting slides. This can make users feel uneasy as they try to rush through the slide’s text before it rotates. Of course auto-rotating too slowly will have the opposite effect, with users getting bored by slides that are of little interest to them.
The amount of text in each slide has a significant say in the duration a slide should be shown. If there’s just a short header, 5-7 seconds proved appropriate during test, while longer durations were needed for more text-heavy slides.
You can see more here:
Here you can find guidelines for good carousel design: https://www.nngroup.com/articles/designing-effective-carousels/
And here about the carousel's time: https://baymard.com/blog/homepage-carousel
I hope it helps.