Proofreading...

The patient was being seen for an injured left ankle he suffered during a motorcycle accident (On a dirt race track, I believe.) This patient has a longstanding history of depression and has expressed thoughts of suicidal ideation [which seemed to peak about a year ago after his girlfriend died.]
Correct
The patient was being seen for an injured left ankle he suffered during a motorcycle accident (on a dirt race track, I believe.) This patient has a longstanding (history of depression and has expressed thoughts of suicidal ideation) [which seemed to peak about a year ago after his girlfriend died.]

This patient is a 33-year-old female who states that she began to have problems with her balance approximately 8 years ago (her complaints began after a head trauma.) Her complaints consist of fatiguing easily after prolonged activity and losing her balance during ambulation easily. (she has been a distance runner for years)

Correct
This patient is a 33-year-old female who states that she began to have problems with her balance approximately 8 years ago (her complaints began after a head trauma.) (Her complaints consist of fatiguing easily after prolonged activity and losing her balance) during ambulation easily. (She has been a distance runner for years.)

Im confuse can someone explain it to me?

You've posted two paragraphs with errors in them and two that have supposedly been corrected.

What directions have you been given? What are you supposed to do with these?

When using parentheses, if you have a parenthetical idea within a parenthetical idea, you would use brackets inside of parentheses.

They want me to correct the paragraphs with parentheses or brackets inside of parentheses, but I don't understand it that well and I been going over it over a weeks or so.

Sure! Let's go through the proofreading corrections for each sentence to help clarify them:

1. The original sentence is: "The patient was being seen for an injured left ankle he suffered during a motorcycle accident (On a dirt track, I believe.) This patient has a longstanding (history of depression and has expressed thoughts of suicidal ideation) [which seemed to peak about a year ago after his girlfriend died.]"

The corrected sentence is: "The patient was being seen for an injured left ankle he suffered during a motorcycle accident (on a dirt race track, I believe.) This patient has a longstanding (history of depression and has expressed thoughts of suicidal ideation) [which seemed to peak about a year ago after his girlfriend died.]"

In this correction, the main change is the capitalization of "on" in "on a dirt race track" as it is part of the sentence rather than a separate reference. The rest of the sentence remains the same.

2. The original sentence is: "This patient is a 33-year-old female who states that she began to have problems with her balance approximately 8 years ago (her complaints began after a head trauma.) Her complaints consist of fatiguing easily after prolonged activity and losing her balance during ambulation easily. (she has been a distance runner for years)"

The corrected sentence is: "This patient is a 33-year-old female who states that she began to have problems with her balance approximately 8 years ago (her complaints began after a head trauma.) (Her complaints consist of fatiguing easily after prolonged activity and losing her balance) during ambulation easily. (She has been a distance runner for years.)"

In this correction, the parentheses have been added to indicate that "during ambulation easily" is referring to the previous clause "losing her balance." This helps make it clearer that the patient loses balance while walking. Additionally, the sentence about being a distance runner has been placed in parentheses to separate it from the rest of the sentence.

I hope this explanation helps clarify the proofreading corrections. Let me know if you have any other questions!