“Did you have a rough day?”
You're having dinner with your wife. She looks tired and unhappy. You guess that she might have had some problems at work. You ask her this because you're concerned.
Did you have a rough day?
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Did (something happen)?
In this sentence, the speaker asks "Did you..."" instead of "Have you...?" That's because the day is already almost over.
If you ask someone about their day when it's still noon or 2:00, you can ask instead:
Have you had a rough day?
a rough day
A "rough" day is one in which you have a lot of problems, or feel tired and stressed. People especially talk about having a "rough day" at work:
A: Rough day?
B: Yeah, my boss yelled at me for something that wasn't even my fault.
If you want to talk about more than one day, you don't say "rough days". You say "a rough few days" or "a rough couple of days":
Sorry I didn't call you back earlier. I've had a rough couple of days.
The word "rough" can mean "difficult" or "filled with problems" in some situations. Here are some things that people often describe as "rough":
(a company) is going through a rough period
(someone) is going through a rough time
we got off to a rough start