C

Step 1: Identify the variables given in the problem:
- Speed of the galaxy, v = 286 \text{ km/s} = 286 \times 10^3 \text{ m/s}
- Wavelength of the light emitted, \lambda_0 = 630 \text{ nm} = 630 \times 10^{-9} \text{ m}
- Speed of light, c = 3 \times 10^8 \text{ m/s}

Step 2: Calculate the observed wavelength, \lambda, using the formula for redshift:
\[ z = \frac{\lambda - \lambda_0}{\lambda_0} = \frac{v}{c} \]
Rearranging gives us: \[ \lambda = \lambda_0 \left( 1 + \frac{v}{c} \right)
= 630 \times 10^{-9} \text{ m} \left( 1 + \frac{286 \times 10^3}{3 \times 10^8} \right)
= 630 \times 10^{-9} \text{ m} \left( 1 + 0.000952 \right)
= 630 \times 10^{-9} \text{ m} \times 1.000952
= 630.6 \times 10^{-9} \text{ m}
\]

Step 3: Calculate the value of x:
\[ \lambda - \lambda_0 = 630.6 \times 10^{-9} - 630 \times 10^{-9} = 0.6 \times 10^{-9} \text{ m} \]
The value of x is given by \[ \frac{\lambda - \lambda_0}{10^{-10}} = 6 \]
Therefore, the value of x, to the nearest integer, is 6.
So the answer is x = 6.