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This is in the following context:

$$ q(t;\theta) = P(T=t;\theta) = \sum_{\{\textbf{x}:T(\textbf{x})=t\}} f(\textbf{x}; \theta) $$

Where $T=T(\textbf{X})$ is a statistic, $q(t; \theta)$ is the pmf of $T$, $X_1, X_2, ..., X_n$ is a random sample and $f(\textbf{x}; \theta)$ is the pmf of $\textbf{X}$.

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This is simply summing the probabilities of all combinations of $X$ that lead to $T(X)=t$, since it asks for $P(T(X)=t)$. For example, $T=X_1+X_2$: a statistic with respect to the outcome of the two dice, $X_1,X_2$ are face values, and $t$, e.g. $10$ is the sum of them. You'll have the following sum, $\sum_{X_1+X_2=t}P(X_1,X_2)$ that resembles your general sum.

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This simply means sum up the values of the function $ f(\textbf{x}; \theta)$ over all values of $\textbf{x}$ where the test statistic $\textbf{T(x)}=t$

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