Answer
See below.
Work Step by Step
According to the Binomial Theorem we can obtain the $r+1$th term of the expansion of the binomial $(x+y)^n$ by the formula $_nC_rx^{n-r}y^r$.
Hence here it is: (by plugging in $n=10,r=4$ and $x,3$: $_{10}C_4(x)^{10-4}3^4=210x^6\cdot81=17010x^6$, thus the coefficient is $17010$.
