Use periodic trend of electronegativity
Electronegativity generally:

• increases across a period from left to right
• decreases down a group

Identify approximate electronegativities
The given elements are:

• $\mathrm{Br}$ (bromine)
• $\mathrm{C}$ (carbon)
• $\mathrm{At}$ (astatine)
• $\mathrm{P}$ (phosphorus)

Approximate Pauling electronegativities are:

• $\mathrm{Br} \approx 2.8$
• $\mathrm{C} \approx 2.5$
• $\mathrm{At} \approx 2.2$
• $\mathrm{P} \approx 2.1$

Arrange in decreasing order
Therefore, $\mathrm{Br} > \mathrm{C} > \mathrm{At} > \mathrm{P}$

Check the options

• A: $\mathrm{C}>\mathrm{P}>\mathrm{At}>\mathrm{Br}$ ❌
• B: $\mathrm{Br}>\mathrm{C}>\mathrm{At}>\mathrm{P}$ ✅
• C: $\mathrm{Br}>\mathrm{P}>\mathrm{At}>\mathrm{C}$ ❌
• D: $\mathrm{P}>\mathrm{Br}>\mathrm{C}>\mathrm{At}$ ❌

Final answer
The correct order is: $\boxed{\mathrm{Br}>\mathrm{C}>\mathrm{At}>\mathrm{P}}$ So, the correct option is B.