The fundamental counting principle says we can just multiply the number of options in each category to find the total number of possibilities. (A simpler example of this concept is that is we have 5 shirts and 7 pairs of pants, we can create 35 distinct outfits.)
The wording "at most one dish" makes it sound like it is possible to order no dishes of a certain variety, so we should add one to each list of options: 8 chicken choices (including not ordering chicken), 6 beef choices, etc.
This interpretation yields 8 x 6 x 5 x 11 = 2,640 options (though 1 of these options would be not ordering anything, which doesn't seem like a valid way to order).
By the way, if we instead read the question to mean exactly one of each type must be ordered, then we would instead calculate 7 x 5 x 4 x 10 = 1,400 distinct options.
