Answer
$2.44*10^{-6} m$
Work Step by Step
The equation for a maxima in a diffraction grating system is given by
$$dsin\theta=m\lambda$$
where $d$ is the grating spacing, $\theta$ is the angle from the diffraction grating at which the maxima forms, $m$ is the order of the maxima fringe, and $\lambda$ is the light wavelength.
In this question, $m=1$, $\lambda=550nm$. We are told that the angle between the first order maxima at opposite sides of the zeroth order maximum is $26$ degrees, hence the angle between either maxima and the central maximum is half that. Hence, $\theta=13$ degrees.
Now that we have all our values we can find $d$
$$d=\frac{m\lambda}{sin\theta}=\frac{1*550*10^{-9}}{sin(13)}=2.44*10^{-6} m$$
