Answer
$17010A^6B^4$
Work Step by Step
Step 1. With the Binomial Theorem, the $r$th term of the expansion of $(a+b)^n$ is given by:
$\begin{pmatrix} n\\r-1 \end{pmatrix}a^{n-r+1}b^{r-1}$
Step 2. With $n=10$, replace $a$ with $A$ and the term containing $A^6$ gives $n-r+1=6$ or $r=10+1-6=5$
Step 3. We can write the term containing $A^6$ as:
$\begin{pmatrix} 10\\5-1 \end{pmatrix}A^{10-5+1}(3B)^{5-1}=210A^63^4B^4=17010A^6B^4$
