The given expression as;
[tex]\frac{2\sqrt[]{x+4}}{3}=6[/tex]
Squaring both side;
[tex]\begin{gathered} \mleft\lbrace\frac{2\sqrt[]{x+4}}{3}\mright\rbrace^2=6^2 \\ \frac{2^2(x+4)}{3^2}=36 \\ \frac{4(x+4)}{9}=36 \\ 4(x+4)=36\times9 \\ 4x+16=324 \\ 4x=324-16 \\ 4x=308 \\ x=\frac{308}{4} \\ x=77 \end{gathered}[/tex]
Answer : x = 77
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