Answer
The quark makeup of $\bar{K^0}$ is $~~s\bar{d}$
Work Step by Step
Each spin-zero meson is made up of one quark and one antiquark.
The $\bar{K^0}$ has charge $0$, strangeness $-1$, and baryon number $0$
If the strangeness is $-1$, then there must be one strange quark.
The strange quark $s$ has charge $-\frac{1}{3}$, strangeness $-1$, and baryon number $+\frac{1}{3}$
The antiquark $\bar{d}$ has charge $+\frac{1}{3}$, strangeness $0$, and baryon number $-\frac{1}{3}$
Therefore, the quark makeup of $\bar{K^0}$ is $~~s\bar{d}$.