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If you carefully look at the given $\epsilon$- NFA it is accepting  $x^{*}$ and $\epsilon$ and $y^{*}$ i.e.$x^{n}y^{m}$ where n>=0 and m>=0 but not $y^{m}x^{n}$.

So its NFA will be

Now we can convert this NFA by defining transition for each state. For state A transition for x and y are defined but for B state transition for x is not defined so we have to add a dead state.

hence the DFA will be

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