A plane has equation [tex]ax+by+cz=d[/tex]. With the given information, you should be able to find the values of [tex]a,b,c,d[/tex].
Since the plane contains the points [tex](3,0,0)[/tex], you have
[tex]a\times3+b\times0+c\times0=3a=d[/tex]
The other points tell you that you have
[tex]8b=d[/tex]
[tex]6c=d[/tex]
So, [tex]3a=8b=6c[/tex], or, fixing [tex]a[/tex], you get [tex]b=\dfrac38a[/tex], [tex]c=\dfrac12a[/tex], and [tex]d=3a[/tex], giving the equation
[tex]ax+\dfrac38ay+\dfrac12az=3a\implies x+\dfrac38y+\dfrac12z=3\implies 8x+3y+4z=24[/tex]
