Let's follow the steps given.
First it asks to rewrite the square root. So:
[tex]\sqrt[]{x^3}=\sqrt[]{x^2\cdot x}=\sqrt[]{x^2}\cdot\sqrt[]{x}[/tex]Thus:
[tex]6\sqrt[]{x^3}+8x\sqrt[]{x}=6\sqrt[]{x^2}\sqrt[]{x}+8x\sqrt[]{x}[/tex]Then, it asks to simplify the square root:
[tex]\sqrt[]{x^2}=x[/tex]Thus:
[tex]6\sqrt[]{x^2}\sqrt[]{x}+8x\sqrt[]{x}=6x\sqrt[]{x}+8x\sqrt[]{x}[/tex]Now, we use the distributive property backwards:
[tex]6x\sqrt[]{x}+8x\sqrt[]{x}=(6x+8x)\sqrt[]{x}[/tex]Finally, we add what is inside of the parenthesis:
[tex](6x+8x)\sqrt[]{x}=14x\sqrt[]{x}[/tex]