Show the vibrational frequency of fluorine molecule anion is much lower than that of fluorine molecule
You should definitely post the MO diagram of $\ce{F2}$ that you worked out. When trying to solve such a problem you should try to analyse the question as thoroughly as possible to make sure that you collect all the information available to you beforehand. Especially important here is that the question already tells you that the vibrational frequency of $\ce{F2^{-}}$ is lower than that of $\ce{F2}$. So the first question you should ask yourself is: Under what circumstances is a vibrational frequency lowered and which relation do I know that links the vibrational frequency to some variable that is connected to the MO diagram of $\ce{F2}$? I give you a hint: You will need the equation of a harmonic oscillator

\begin{equation}
 \omega = \sqrt{\frac{k}{m}}
\end{equation}

where $\omega = 2 \pi f$ is the angular frequency, $f$ is the frequency, $k$ is the force constant (in your case of the bond and thus its a measure of the bond strength) and $m$ is the reduced mass of the oscillating system. (The harmonic oscillator is one of those simple model systems that can help you quite often when you want a starting point for the investigation of much more complicated ones.) Now ask yourself: Which of the variables $k$ or $m$ might have a relation to the MO diagram and how will they be related?