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Give an explanation why $\ce{MgF2}$ and $\ce{CaF2}$ adopt different structure types.
For example, the structure of calcium fluoride is 'fluorite' and the structure of magnesium fluoride is 'rutile'. I am struggling, just from looking at the formulae, on how I determine this?
I'll just point out the direction in which you could look for an answer.
In general case, it should be almost impossible to determine the crystal structure by looking at the chemical composition of a substance.
You are, however, asked to explain why different fluorides adopt different structure types, which is a different task. Perhaps, you should take into account the difference (sorry) in the ionic radii of Mg and Ca. Some structures prefer "fat" cations, some - "lean" ones. Most of the time, it's just plain geometry combined with experimental observations. I know the explanation is primitive, and ions are not just some rigid spheres, but the "ionic radii" approach works in many cases.
For many crystal structures there are ranges of ionic radii ratios in which the particular structure is more or less stable. Some of these ratios are so important that they have proper names, such as Goldschmidt tolerance factor for perovskites. Returning to your example, this page lists the cation/anion radii ratios for fluorite (0.73 or above) and rutile (between 0.41 and 0.73). You can check these ratios against the dimensions of ions in magnesium and calcium fluorites.
For the reference - this Shannon table hosted by Imperial College London is an excellent source of the values of ionic radii in oxides and halides. Just one more thing: the reference ratios are likely to be designed to work with so-called Shannon Ionic Radii, not the less-common Shannon Crystal Radii.
Not really a complete answer, rather an addition to the given answer (which I think you should accept). As of now, it's possible to predict existence of certain compounds, mostly binary and ternary inorganic ionic solids, at the given temperature and pressure, as well as their crystal structure.
There are many computer programs, among which USPEX is arguably the most feature-rich and promoted. It uses Oganov-Glass evolutionary algorithm and works best for network solids (including particles and clusters). Fairly recently there also were some advancements for predicting crystal structures of small organic molecules.
You can treat it as a "generic problem solving" type of question. @voffch gave some specific ways to do this.
You're asked why they form different structures, but don't have to say anything about their actual structures. This question sounds like something from an introductory undergrad general/inorganic course or high school honors gen chem course. Typical material for such a course discusses ionic structures in terms of sphere packing/ionic radius (keywords: fcc, bcc, hcp) and covers ionic radius in terms of electronegativity and shielding.
You're given:
So the question is implicitly "Of the differences between Mg and Ca cations, which differences make their fluorides have different structures?."
The specific mention of F suggests there's something special about it too. F is pretty "extreme" all the way in its corner so it was probably chosen as a "superlative," e.g. "most electronegative," "smallest, "biggest occupational hazard" or something like that.
At this point, you can just compile a list of all the things you've learned about metal/halide ions over the relevant time period and pick ones that affect geometry. Also consider what you've been taught about crystal structures.
It could play out like this:
By way of explanation, you can explain radius trends + draw a sketch of the different packings, approximately to scale.
If your course covered different material-- Compare Mg, Ca in terms of the stuff your course covered.
