We don't need to know any unknowns!

We have: $3m+2n+4s=26........ (1)$
$6n+4m+2s=48........ (2)$

Dividing $(2)$ by 2; we get:
$3n+2m+s=24.......... (3)$

Adding $(1)$ and $(3)$ ; we get:
$5m+5n+5s=50$
$\implies \boxed{m+n+s=10}$

$\begin{aligned} 3m + 2n + 4s & = 26 & ...(1) \end{aligned}$

$\begin{aligned} 4m + 6n + 2s & = 48 & \small \color{#3D99F6} \text{Divide both sides by }2 \\ 2m + 3n + s & = 24 & ...(2) \end{aligned}$

$\begin{aligned} (1) + (2): \quad 5m + 5n + 5s & = 50 & \small \color{#3D99F6} \text{Divide both sides by }5 \\ \implies m+n+s & = \boxed{10} \end{aligned}$

4m+6n+2s=48(a) & 3m +2n + 4s =26(b)
subtracting equation (b) from (a)
we get ,m+4n-2s=22
therefore,3m+12n-6s=66(c)
subtracting equation (b) from equation (c)
we get,b-c=4(d)
subtracting equation (d) from equation (b)
we get , 3m+3n +3s=30, =>m+n+s=10

(2m+3n+s) 3=24 3........(1) (3m+2n+4s) 2=26 3.......(2) (1)-(2) n-s=4........(3) 3m+2n+4s=26.......(4) 4m+6n+2s=48........(5) (5)-(4) m+4n-2s=22 m+2n+2(n-s)=22 m+2n=22-2*4 m+2n=14 m+n+n=14 m+n=14-n m+n+s=14-(n-s) m+n+s=10