This is a fairly common style of a synthesis where students are asked to make a more complex molecule from a simple alkane.
The key in this synthesis is to recognize that we’re cutting through the C-C bond. The main method of C-C bond cutting in an undergraduate curriculum is the ozonolysis reaction. But first, we need to make an alkene. Of course, there’s no direct way how we can convert an alkane into alkene. However, if we had a leaving group, we could perform an elimination reaction. And to get the leaving group onto an alkane, we’re going to do the only reaction that alkanes do − radical halogenation!
And once we have the overall pattern for our synthesis, we can put it all together.