After the men talk, Levin goes to the drawing room, where he knows Kitty is, and they communicate in a nearly wordless fashion. Levin writes the initial letters of each word of a sentence on the table in chalk. Kitty understands him precisely and replies in the same fashion. In the same, nearly wordless but deeply understood way, Levin and Kitty admit their love for each other. Levin proposes and Kitty accepts. Though very little was said in words, everything important was communicated and understood fully.
Though Tolstoy is rather verbose in his writing, he distrusts excessive use of language, and his characters are most truly in sync with each other when they can communicate wordlessly. Levin proposes in code, and Kitty understands him so deeply that she replies in code. Their love is so deep that it goes beyond language.