Homework ? really struggling on the whole concept

The data in the stem-and-leaf plot (from least to greatest for easier organization) is:
75, 75, 84, 87, 96

(Stem and leaf plots are read from left to right, like tens place and then you add the number on the right to it. That is the one's place number.) 

Number 1 asks for the median, and in this case, it has to be 85% or higher for you to answer "yes".
The median from this data set is the number "84".
Therefore, your answer will be "No."

Number 2 asks for the score that he should have on his last exam. That answer will be determined by doing as follows:
75+75+84+87+96+x (undetermined last quiz that we are finding.)
   =    85 (the average that should be found.)
               6

Now, in the start of this system or equation, you don't divide all of the numbers by 6. You add the numbers together (the numerator) and that should leave you with:
417+x     = 85

     6

With this, you still won't divide in the fraction by 6. You'll multiply the denominator by 6 to cancel the denominator to make the equation easier to solve. 
That will leave you with 417+x = 85.

Then, multiply the 85 by 6, since you did it to the denominator. That will give you 510. 

Your equation should now be 417+x=510.
To solve, simply subtract 510-417, and you should get 93. 
For number 2, your final answer should be a score of 93 to get 85 as an average. 

The last answer would be set up like 75+75+84+87+96+90
                                                                = (the mean)
                                                                                  6
That is 84.5. 
That means that he wont be reimbursed. 
His average is 84.5.

If you need to, then round to the nearest tenth.

Hope I could help you ;)