The reagent X in the reactions
`(CH_3)_3C CH=CH_2 underset"THF"oversetX to Y underset"NaOH"overset(NaBH_2)to (CH_3)_3-undersetunderset(OH)(|)C-CH-CH_3`

Options

A. `H_3O^+`
B. `Hg(CH_3COO)_2`
C. `OH^-`
D. HCOOH

Explanation

To solve the problem, we need to identify the reagent \( X \) used in the reaction involving the compound \( (CH_3)_3C-CH=CH_2 \) and how it leads to the final product.

### Step-by-Step Solution:

1. **Identify the Starting Material**:
The starting material is \( (CH_3)_3C-CH=CH_2 \). This compound is an alkene with a tertiary butyl group attached to a double bond.

2. **Understanding the Reaction Conditions**:
The reaction takes place in the presence of THF (tetrahydrofuran), which is a common solvent used in organic reactions. The presence of THF suggests that the reaction may involve a transition state or intermediate that is stabilized in this solvent.

3. **Determine the Type of Reaction**:
The reaction involves the addition of a reagent \( X \) to the alkene. Given that the product involves the formation of an alcohol, we can infer that this is likely a hydration reaction.

4. **Identify the Reagent \( X \)**:
For hydration of alkenes, a common method involves the use of mercuric salts, such as mercuric acetate (\( Hg(OAc)_2 \)) or mercuric sulfate (\( HgSO_4 \)). These reagents form a mercurinium ion intermediate, which is then attacked by water to form an alcohol.

5. **Reaction with \( NaOH \) and \( NaBH_2 \)**:
After the addition of \( X \), the product \( Y \) undergoes further reactions with \( NaOH \) and \( NaBH_2 \). The \( NaOH \) likely serves to deprotonate the alcohol formed, while \( NaBH_2 \) is a reducing agent that can reduce any carbonyl groups present, but in this case, it is used to stabilize the alcohol.

6. **Final Product Structure**:
The final product is \( (CH_3)_3C-CH(OH)-CH_3 \), indicating that the alcohol is formed on the carbon that was part of the double bond, and the structure confirms that the tertiary carbon retains its three methyl groups.

### Conclusion:
The reagent \( X \) in the reaction is \( HgSO_4 \) or a similar mercuric salt, which facilitates the hydration of the alkene to form the alcohol.