1. Recall the definition of Young's modulus

   Young's modulus is a material property defined as $Y = \frac{\text{stress}}{\text{strain}} = \frac{F/A}{\Delta L/L} = \frac{FL}{A\,\Delta L}.$

2. Key idea

   Young's modulus depends only on the nature of the material (and temperature), not on the dimensions of the wire.

   So changing:

   • length from $L$ to $2L$
   • area from $A$ to $A/2$

   does not change the value of Young's modulus.

3. Therefore

   The new Young's modulus remains $Y.$

4. Check options

   • A: $4Y$ ✗
   • B: $2Y$ ✗
   • C: $\dfrac{Y}{4}$ ✗
   • D: $Y$ ✓

Hence, the correct answer is Option D.