= Solution
A formula $\phi(\bar x,\bar y)$ has the <order property> for $T$ when, for every finite $n$, some model contains tuples $a_i,b_j$ with
$$
\phi(a_i,b_j)\quad\Longleftrightarrow\quad i<j.
$$
Compactness realizes this pattern indexed by any linear order.
Fix $\kappa\geq|T|$ and let $\lambda$ be least with $2^\lambda>\kappa$. Use the order property along $I=\mathbb Q^\lambda$, and take parameters
$$
B=\{b_j:j\in J\},
$$
where part i gives $|B|\leq\kappa$. For distinct $i,i'\in I$, choose $j\in J$ strictly between them. Then $\phi(a_i,b_j)$ and $\phi(a_{i'},b_j)$ have different truth values, so the types $\operatorname{tp}(a_i/B)$ are distinct. There are $|I|=2^\lambda>\kappa$ such types over at most $\kappa$ parameters. Enlarging $B$ to size exactly $\kappa$ if necessary preserves them. Hence $T$ is not $\kappa$-stable. This is the <order property implies instability> argument.
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