As illustrated in the figure, a block of mass m_1 is fastened to a...

Consider the blocks $m_1$ and $m_2$ as a single system of mass $(m_1 + m_2)$.

In the equilibrium position, the net force acting on the system along the inclined plane is zero.

The downward force along the incline due to gravity is $(m_1 + m_2)g \sin\theta$.

The upward force along the incline due to the compressed spring is $kx$, where $x$ is the compression of the spring.

Equating these forces:

$kx = (m_1 + m_2)g \sin\theta$

$x = \dfrac{(m_1 + m_2)g \sin\theta}{k}$