what is the mode and median of this set of numbers 22,33,43,65,676,33

Alan's median is correct.

It is really good to remember that if there are n numbers, the middle position will be the (n+1)/2 position

In this example there are 6 numbers.  

The middle position is (6+1)/2=3.5  SO the median will be the average of the 3rd and 4th scores.

This is really handy knowledge when there are a lot of scores.

To answer this question, you will need to know what Mode and Median is. Let me run you through. Mode is the number that appears the most in a series of numbers. For Example:

11,22,33,44,55,66,77,88,11,22,11,99

The Mode of this series of Numbers in 11, because it appears the most out the rest of the numbers.
11 Appears 3 Times and 22 Appears Twice.

Median is the centre number when arranged in order. Lets use the series I chose.

I placed them in order:

11,11,11,22,22,33,44,55,66,77,88,99

Now which one is the middle number?

33!

Now, lets use your series:

22,33,43,65,676,33

33 Appears the most, so the mode is 33

22,33,33,43,65,676 (I placed them in order)

For the Median, you may choose 33 or 43 
But for the make of 6 Divided by 2 is 3, I'll choose the 3rd number.

The Mode is 33 and the Median is 33

In the case when there is an even number of numbers it is normal to take the median as the average of the two nearest the middle.  So, in this case the median would be (33+43)/2 = 38