come across (something)

This phrase means to find something without really trying to look for it:

But sometimes you'll be flipping through the channels and come across something really interesting.

Aren't these great? I came across them at a thrift shop a couple weeks ago.

an article about how (sentence)

You may want to explain articles that you read in magazines, newspapers, and on the Internet.

When you just want to tell someone the topic of the article, you can say it like this:

I just read an article about the upcoming U.S. election. 

But if you want to explain what the article is saying about the topic, you use "about how" followed by a complete sentence:

I just read an article about how people are using a betting market to try to predict the upcoming U.S. election.

(do something) for long periods

Doing something for "long periods" means that you do it for a long time without stopping.

For example, if you have to stand up at work and don't get a chance to sit down for a few hours, you can say that you "stand for long periods" at your job.

(something) is horrible for your health

"Horrible" means "really bad".

Something that will hurt your body is "horrible for your health". Things that are horrible for your health include:

• smoking
• working around dangerous chemicals
• working really long hours each day

supposedly (adjective)

Use this phrase to talk about something that other people say is true. You might believe them or might not. For example:

I have some old comic books from when I was a kid that are supposedly worth a lot of money. I've never tried to sell them, though, so I don't know.