The conversation goes something like this:
Woman: I'll change the bed sheets.
Man: No, I'll do it!
Woman: I can make a bed!
Man : You wouldn't know a hospital corner if it bit you on the arse.
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(You) wouldn't know (x) if (y)... is a relatively common way to express that the other person is unfamiliar with something. In this case it's a particular way to do up sheets on a bed.
If something bites you in the arse, trips you, or hits you in the face, it's presumed you'd recognize it on sight or by feel (as in, a dog bite).
- You wouldn't know a hospital corner if it bit you on the ass. (I'm AmE)
- You wouldn't know a hospital corner if you tripped over it.
- You wouldn't know a hospital corner if it smacked you in the face.
- You wouldn't know a hospital corner if it hit you on the head.
Some examples from the internet:
- You wouldn't know kindness if it tap-danced in front of your nose.
- You wouldn't know love if it hit you in the face with a shovel.
- You wouldn't know God if He walked up and introduced himself.
- You wouldn't know good music if it came up to you and said, "Hello I'm good music".
I assume it's the 'hospital corner' reference you are having a problem with.
There's a useful explanation here, from which I have quoted the following excerpt:
The bed-making technique of folding hospital corners originates back to the 19th century and the profession of nursing. Nursing is a profession with a long history that was built on war-time and the military. During the 1850s, Florence Nightingale famously organized a group of women to aid the wounded during the Crimean War. Working for and assisting soldiers and doctors demanded nurses to be efficient, clean and organized in the war hospital. With a single sheet, hospital corners were used not only to keep the sheet firmly in place, but also allow nurses to easily change or resize the sheet without causing discomfort to the patient. (Note: The fitted sheet as we know it with its elastic corners would not be invented until the 1990s).
The same page also contains an instructional video which demonstrates how to make hospital corners.
However, if you prefer a step-by-step explanation with individual photos, you will find a good one here.