Which sentence is punctuated correctly?
my father loved talking about history, particularly: the civil war, the cold war, and the revolutionary war.
there were several scientific processes i wanted to learn about such as, photosynthesis, diffusion, and osmosis.
the only states that marina had yet to visit were: colorado, wyoming, north dakota, and rhode island.
when studying mythology, i learned about several gods and goddesses: zeus, apollo, aphrodite, hermes, and hercules.

The sentence which has been correctly punctuated is THE LAST ONE.

The last question is well punctuated because it has a comma after the initial adverbial phrase, and then it has a colon to introduce an enumerating list. In addition, the items enumerated are separated by commas which is also correct.

hmm, sadly there is no dialogue. there is no place in the story where he is talking to anyone. it's more of just describing what he eats and where he sleeps. you have to become anne frank, give details of where you are, what other folks look like, how the environment is. have a little bit of dialogue tell of what people are specifically saying. anne frank talked about her entire household including the people, the objects, the lighting, the food they ate, and even the smell in the air. there has to be more to your diary entries, the whole story in its current state is only about peter van daan, the food, the sounds, and where he sleeps. also he seems to be writing only once a year yet more than that happened from day to day. for a friend, i can you write it out, if you want.