You purchase 500shares of a start-up for $1.34/share. over the next 10 years, the stock splits twice. first, there is a 2: 1 split followed by a 3: 2 split. at the end of the 10 years, the stock is worth $3.15/share. calculate the cagr.

Figure out the splits first. 
A 2:1 split gives him 2 * 500 = 1000 shares.
Now you get a 3:2 split
(3/2) * 1000 = 3000/2 = 1500 shares. 

At the end of ten years he has 1500 shares worth 3.15 / share
Amount = 1500 * 3.15 = 4725 dollars.

His outlay was 500 * 1.34 = 670 dollars. I don't know what CAGR stands for so I don't know how to answer the question
Profit if he sells it = 4725 - 670 = 4055

In summary
Number of shares = 1500
cost of 500 shares = 670
Value of 1500 shares = 4725
Profit over Cost = 4055

You will have go through the summary to figure out what you want.