Is it possible to design $\text{DFA}\{x,y\}$ that has at least $2$ $x$'s and at most $2$ $y$'s?

Question

$L = \{w|$, $w$ has at least $2 x$'s and at most $2 y$'s}

I tried making one but it does not accept aab nor aabb.

If it's possible to draw one, how do you do it? plus is it possible to draw NFA?

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Answer 1

Here each time a $y$ is received, we move down 1 row until we reach $q_9$ (the trash).

Each time an $x$ is received, we move across 1 column until the accepting states.

(Plus it is always possible to draw an NFA first, then convert to DFA.)