Ok. In order to compute the eigenvalues, you set the following determinant,

equal to zero. The equation you get is

The power of each of these factors is its algebraic multiplicity. Hence, is raised to the power 1, and therefore, by definition, the eigenvalue has algebraic multiplicity 1. The factor is raised to the power 2, and therefore, by definition, the eigenvalue has algebraic multiplicity 2.

The geometric multiplicity of an eigenvalue is the dimension of the corresponding eigenspace. When you computed the eigenvectors for you found two linearly independent eigenvectors. Hence, the geometric multiplicity of the eigenvalue is 2. I have a very strong feeling that when you find the eigenvector (which you should do without delay!) corresponding to you will find only one eigenvector. Hence, the geometric multiplicity of the eigenvalue is 1.

These are definitions.

Now, I really think you have enough information to solve this problem completely. Keep your head on the target, which is orthogonally diagonalizing