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