Mnemonic angle: Berkson, admission, hospital go together.
Berkesonian (Berkson's) bias is a selection bias unique to hospital based studies. A patient carrying two diseases is more likely to land in a hospital bed than a patient with a single disease, so hospital samples over represent people with combined conditions. This inflates or fabricates an apparent link between an exposure and a disease that does not exist in the general community.
Since the whole problem comes from unequal hospital admission rates, it is named admission rate bias. The other options do not fit: response bias is about who answers a survey, and reporting bias is about how information gets recorded. So the correct match for admission rate bias is Berkesonian bias.