A bromodichlorobenzene which gives four signals in the broadband proton-decoupled 13C spectrum could be:

See explanation

Explanation:

In this question, we can have several possibilities for the bromodichlorobenzene that depends on the position of the Br and Cl in the benzene. Our options are:

a) 2-bromo-1,3-dichlorobenzene

b) 1-bromo-2,4-dichlorobenzene

c) 1-bromo-2,3-dichlorobenzene

d) 1-bromo-2,3-dichlorobenzene

e) 4-bromo-1,2-dichlorobenzene

See figure 1

Now, if only have 4 signals, we will have only 4 different types of carbons. In benzene we have 6 carbons, therefore, we will have symmetry in the molecule and some of the carbons would be equivalent. The only molecule that has symmetry is "2-bromo-1,3-dichlorobenzene" because we have several carbons with the same neighbors (see figure 2).

Finally, to check the molecule we can check the 13C NMR for 2-bromo-1,3-dichlorobenzene and we will see that only have 4 signals (see figure 3)