Think of a wire as a water pipe; making it longer increases the distance water must travel, and making it narrower restricts the flow much more significantly, creating a compounded effect on the total resistance.

L-R-A: Length increases Resistance, Radius (squared) decreases Resistance.

The resistance $R$ of a wire is given by $R = \rho \frac{L}{A}$, where $A = \pi r^2$. Substituting the new values $L' = 2L$ and $r' = r/2$, the new area becomes $A' = \pi (r/2)^2 = \frac{\pi r^2}{4}$. Thus, the new resistance $R' = \rho \frac{2L}{A/4} = 8 imes (\rho \frac{L}{A}) = 8R$.

When dealing with wire stretching or modification problems, always remember that radius changes affect the area quadratically ($r^2$), which is the most common area of error in competitive exams.