This is another one of those finicky little rules that have the potential to show up on the SAT and ACT. It’s an annoying one because it involves not one but two kinds of punctuation, in this case commas and parentheses (which aren’t tested all that frequently), but it’s not overly tricky to apply. In fact, if you look back at the previous sentence, you’ll see that I just used it.

Here’s the whole rule:

It is never acceptable to use a comma before an open parenthesis, but it is sometimes acceptable to use a comma after a close parenthesis.

In other words, the construction below is always incorrect:

Incorrect: The Caribbean Sea contains some of the world’s most stunning coral reefs, (which are home to thousands of species of marine life) but many of them are in danger because of overfishing and pollution.

It also means that you cannot do the following:

Incorrect: The Caribbean Sea contains some of the world’s most stunning coral reefs, (which are home to thousands of species of marine life), but many of them are in danger because of overfishing and pollution.

Why? Because two commas = two parentheses. Either type of punctuation can be used to set off a non-essential clause, but it is redundant to use both.

On the other hand, this is perfectly fine:

Correct: The Caribbean Sea contains some of the world’s most stunning coral reefs (which are home to thousands of species of marine life), but many of them are in danger because of overfishing and pollution.

In this case, the comma after the close-parenthesis is all right because a comma would be necessary if the parentheses were eliminated. In that case, we would be left with two complete sentences joined by the coordinating conjunction but — a construction that requires a comma.

Correct: The Caribbean Sea contains some of the world’s most stunning coral reefs, but many of them are in danger because of overfishing and pollution.