Assuming that the photos are tagged with the name of the person as keyword you can do it with these two ways:

Using the Textsearch:

• Go to the library menu in Lightroom.
• Select the library filter "Text".
• Set the first dropdown field to "Keywords". (Default "Any Searchable Field")
• Set the second dropdown field to "Contains Words". (Default "Contain All"?)
• Enter your search in the textfield next to it : Mary, Frank
• Lightroom should now display all photos containing the keywords "Mary" AND "Frank"

Using the Metadata filter:

• Go to the library menu in Lightroom.
• Select the library filter "Metadata" you should see multiple filters for different types (e.g. Date, Camera ...)
• Click on the name of one of those filters (e.g. date), select keyword as new filter type
• Set another filter to be a keyword filter. You should now have two filters where you can see your keywords.
• Select the first keyword you are looking for ("Mary") in one filter. The other keyword filter should now show less keywords, as it will only show keywords of photos which also have the keyword "Mary.
• Select the second keyword ("Frank") in the other filter, where you did not select Mary.
• Lightroom should now display all photos containing the keywords "Mary" AND "Frank"

You can extend this with more keyword filters if you look for more persons. If you select multiple values in one filter, Lightroom will show all photos which include atleast one of them (OR).

The first approach should be easier and faster. The metadata filter approach can be interesting for browsing.