I suppose you have some (course) notes on the topic? You find the eigenvalues by solving: $$\det\left(A-\lambda I_n\right)=0$$ where $A$ is the $n\times n$-matrix given and $I_n$ is the identity matrix. In your case, this means solving: $$\begin{vmatrix} 8-\lambda & -6 & 2 \\\ -6& 7-\lambda & -4 \\\ 2 & -4 & 3-\lambda \end{vmatrix}=0$$
> I've tried add/substract rows and columns and the way this pdf shows
Do you know how to calculate a ($3 \times 3$) determinant?
You can use properties of determinants to try and simplify the calculations, but you can also go for the straightforward calculation by expanding along a column or row of your choice: that will lead to a 3rd degree polynomial equation in $\lambda$.