The following sentence is amiguous. Provide two explanations which illustrate the different meanings Visiting relatives can be problematic.

This kind of sentence is such an interesting example of the complexity of the English language.  Let's go over the two meanings this sentence has.
One way to read this sentence is to interpret it to mean that when we go to visit our relatives, it can be a problem.  In this instance, the word "visiting" is acting like a noun, as it is when we say things like "Cooking is a great hobby" or "Baking fish requires only a moderate oven."  We call words ending in "ing" that are acting as nouns gerunds. 
The other way to read this sentence is to read it to mean that the relatives who come to visit can be a problem.  In this case, the word "visiting" is acting like an adjective, modifying the noun "relatives," and when a verb acts like this, we call it a participle. Many participles end in "ing." Another example of this would be "The crying child needed a hug"  and "The winding path took me far."
There are many entertaining examples of this kind of ambiguous sentence as well as other entertainments that show how interesting English is at the website available at the link below. 
http://www.fun-with-words.com/