You have the following expression:
[tex]14\sqrt[]{6}-6\sqrt[]{24}[/tex]
In order to simplify the previous expression, conisder that 24 can be written as:
24 = 6*4 = 6*2^2
Then, you have:
[tex]\begin{gathered} 14\sqrt[]{6}-6\sqrt[]{24}= \\ 14\sqrt[]{6}-6\sqrt[]{6\cdot2^2}= \\ 14\sqrt[]{6}-6\cdot2\sqrt[]{6}= \\ 14\sqrt[]{6}-12\sqrt[]{6}= \\ 2\sqrt[]{6} \end{gathered}[/tex]
Where in the last steo you simplify the terms becasue they are like terms due to the factor √6.
Then, you have for the required coefficients:
a = 2
b = 6
