Coefficient play

Multinomial theorem plays its role here.

First we need to find the number of terms in expansion ' $m$ ',

Here,

$k$ = Number of terms in polynomial

$n$ = Power of expansion

$m=\dbinom{n+k-1}{n}$

$m=\binom{6}{4}$

$m=15$

Now,

We need to calculate the coefficient of $xy^2z$ ,

General term for expansion of $(3x-4y+6z)^4$ will be $\frac{4!}{a!b!c!}(3x)^a(-4y)^b(6z)^c$ ,

Pluging in the values $a=1$ , $b=2$ and $c=1$ and we get $3456xy^2z$

Hence,

$n=3456$

So,

$m+n=\boxed{3471}$