According to the question,

while B can do it in 6 days, B worked at it only for 4 days,

so, the work completed by B in 4 days$=\frac{1}{6}\times 4=\frac{2}{3}$

Remaining work$=1-\frac{2}{3}=\frac{1}{3}$

A can do this work in 10 days,

So, in 1 day A can complete$\frac{1}{10}$^th of the work

∴ $\frac{1}{3}$^rd of the work is finished by A in $\left(10\times \frac{1}{3}\right)=3\frac{1}{3}$ days

Hence option A is the correct.