To determine the resistance $R$ using Ohm's law, we use the formula:

$R = \frac{V}{I}$

Given:

$V = (200 \pm 4)$ volts

$I = (20 \pm 0.2)$ amperes

First, calculate the nominal value of the resistance:

$$R = \frac{200}{20} = 10 \, \Omega$$

Next, we need to calculate the uncertainty in the resistance. For division, the relative uncertainties add up. The relative uncertainty for voltage is:

$$\frac{\Delta V}{V} = \frac{4}{200} = 0.02$$

and for current:

$$\frac{\Delta I}{I} = \frac{0.2}{20} = 0.01$$

Adding these relative uncertainties gives us the relative uncertainty for the resistance:

$$\frac{\Delta R}{R} = \frac{\Delta V}{V} + \frac{\Delta I}{I} = 0.02 + 0.01 = 0.03$$

Now, we calculate the absolute uncertainty for the resistance:

$$\Delta R = R \times 0.03 = 10 \times 0.03 = 0.3 \, \Omega$$

Therefore, the resistance with its uncertainty is:

$$R = 10 \pm 0.3 \, \Omega$$

Thus, the correct answer is:

Option B $(10 \pm 0.3) \Omega$