Learn Russian: Сегодня она должна чистить сапоги и стирать бельё. - Today she must clean the boots and wash the laundry.

должен (must/have to) acts like a short adjective in Russian, which means it has to agree with the subject in gender and number. Because the subject here is the feminine pronoun она (she), we must use the feminine form должна.

Why is the verb стирать used for "to wash" here instead of мыть?

In Russian, the verb you use for washing depends on what you are washing. стирать is used exclusively for washing clothes, fabrics, or laundry. If she were washing the floor, the dishes, or her hands, you would use мыть.

What case are the words сапоги (boots) and бельё (laundry) in?

They are both in the accusative case because they are the direct objects receiving the actions of cleaning and washing. Since they are inanimate objects, their accusative forms look exactly the same as their basic dictionary (nominative) forms.

Why do we use the imperfective verbs чистить and стирать after должна?

When describing daily chores, general routines, or the process of doing work, Russian usually uses the imperfective aspect. The sentence focuses on the fact that these are her duties for the day, rather than stressing the final, completed result of the tasks.