1. Interpret the formula and requirement

We need the isomer of formula $\mathrm{C_4H_8DBr}$ that has two chiral carbon atoms.

A chiral carbon must be attached to four different groups.

2. Check each option

Option A: $2$-Bromo-$1$-deuterobutane

Structure: $\mathrm{DCH_2-CH(Br)-CH_2-CH_3}$

• Carbon-2 is attached to:
  • $\mathrm{Br}$
  • $\mathrm{H}$
  • $\mathrm{CH_2D}$
  • $\mathrm{CH_2CH_3}$

These are four different groups, so carbon-2 is chiral.

• Carbon-1 is $\mathrm{CH_2D}$, so it has two hydrogens/deuterium arrangement as:
  • $\mathrm{D}$
  • $\mathrm{H}$
  • $\mathrm{H}$
  • bonded carbon

Since two substituents are identical ($\mathrm{H,H}$), carbon-1 is not chiral.

So option A has only one chiral carbon.

Option B: $2$-Bromo-$1$-deutero-$2$-methylpropane

Structure: $\mathrm{DCH_2-C(Br)(CH_3)-CH_3}$

At carbon-2, the substituents are:

• $\mathrm{Br}$
• $\mathrm{CH_2D}$
• $\mathrm{CH_3}$
• $\mathrm{CH_3}$

Two groups are identical ($\mathrm{CH_3}$ and $\mathrm{CH_3}$), so carbon-2 is not chiral.

Carbon-1 is $\mathrm{CH_2D}$, which is also not chiral.

So option B has no chiral carbon.

Option C: $2$-Bromo-$3$-deuterobutane

Structure: $\mathrm{CH_3-CH(Br)-CH(D)-CH_3}$

• Carbon-2 is attached to:
  • $\mathrm{Br}$
  • $\mathrm{H}$
  • $\mathrm{CH_3}$
  • $\mathrm{CH(D)CH_3}$

All four groups are different, so carbon-2 is chiral.

• Carbon-3 is attached to:
  • $\mathrm{D}$
  • $\mathrm{H}$
  • $\mathrm{CH_3}$
  • $\mathrm{CH(Br)CH_3}$

Again, all four groups are different, so carbon-3 is also chiral.

So option C has two chiral carbons.

Option D: $2$-Bromo-$2$-deuterobutane

Structure: $\mathrm{CH_3-C(Br)(D)-CH_2-CH_3}$

At carbon-2, substituents are:

• $\mathrm{Br}$
• $\mathrm{D}$
• $\mathrm{CH_3}$
• $\mathrm{CH_2CH_3}$

These are four different groups, so carbon-2 is chiral.

No other carbon is chiral.

So option D has only one chiral carbon.

3. Conclusion

Only option C has two chiral carbon atoms.

Therefore, the correct answer is: $\boxed{\text{C}}$

4. Comparison with stored correct answer

Stored correct answer: C

My derived answer: C

They match.