The values 2, 6, 10, 14 have a mean of 8.

Step 1. The standard deviation. The squares are $36, 4, 4, 36$, so the variance is $\dfrac{80}{4} = 20$ and the standard deviation is $\sqrt{20} = 4.47$.

Step 2. Add 10. The values become $12, 16, 20, 24$. The gaps are the same, so the standard deviation stays $4.47$.

Step 3. Multiply by 2. The values become $4, 12, 20, 28$. Every gap doubles, so the standard deviation becomes $2 \times 4.47 = 8.94$.