Step 1: Recall Friedel-Crafts reactions.
Friedel-Crafts reactions occur in the presence of anhydrous $\text{AlCl}_3$ and can be of two types:
- \Alkylation: $\text{R-Cl} + \text{Ph-H} \rightarrow \text{Ph-R}$
- \Acylation: $\text{R-COCl} + \text{Ph-H} \rightarrow \text{Ph-COR}$
Step 2: Analyze the given transformation.
The given sequence is:
$\text{Acetophenone} \xrightarrow{\text{Y/AlCl}_3} \text{Intermediate} \xrightarrow{\text{X/AlCl}_3} \text{Toluene}$
The final product is Toluene ($\text{Ph-CH}_3$), while the starting compound is Acetophenone ($\text{Ph-COCH}_3$).
To obtain Toluene from Acetophenone, the carbonyl group ($\text{COCH}_3$) must effectively be replaced by a methyl group ($\text{CH}_3$).
Step 3: Logical reagent sequence.
If $\text{Y} = \text{CH}_3\text{COCl}$ and $\text{X} = \text{CH}_3\text{Cl}$, then:
- First reaction ($\text{Y/AlCl}_3$): Friedel-Crafts acylation adds an acyl group, forming Acetophenone from Benzene.
- Second reaction ($\text{X/AlCl}_3$): Friedel-Crafts alkylation adds a methyl group, forming Toluene from Benzene.
This matches the overall relationship between Toluene and Acetophenone in the sequence.
Step 4: Final conclusion.
Thus, the correct reagents are $\text{X} = \text{CH}_3\text{Cl}$ and $\text{Y} = \text{CH}_3\text{COCl}$.
\[
\boxed{\text{X} = \text{CH}_3\text{Cl}, \text{Y} = \text{CH}_3\text{COCl}}
\]