The volume of the platinum ring can be calculated by subtracting the initial water level (4.0 mL) from the final water level (4.2 mL):

$$V_{ring} = 4.2 \ mL - 4.0 \ mL = 0.2 \ mL$$

$$V_{ring} = 0.2 \ cm^3$$

Step 2: Calculate the mass of the platinum ring.

The mass of the platinum ring can be calculated using the formula:

$$m = \rho \times V$$

where:

* m is the mass in grams (g)

* ρ is the density in grams per cubic centimeter (g/cm3)

* V is the volume in cubic centimeters (cm3)

Substituting the given values into the formula, we get:

$$m = (21 \ g/cm3) \times (0.2 \ cm3)$$

$$m = 4.2 \ g$$

Therefore, the mass of the platinum ring is 4.2 grams.