Compound interest means you gain interest on all your money, even the interest you've gained so far. For example, a $1,000 loan with compound interest of 10% annually. You would owe $1,100 after the first year, but $1,210 after the second. Why not an even $1,200, because you're being charged interest on last years amount not the principle amount.
If you have a 6% interest rate, this refers to your annual interest, but that doesn't mean it's only accrued once a year. If the interest is being compounded quarterly, it means that every quarter (a business term for a quarter of a year, or 3 month) 1.5% interest is being calculated and added to your account. Why 1.5%, because 1.5% per quarter times 4 quarters per year equals 6% per year.
So you start with $7,700.00
Then after one quarter you have $7,700 * 1.015 = $7815.50
After two quarters you have $7815.50 * 1.015 = $7932.73
After three quarters you have $7932.73 * 1.015 = $8051.72
And after a full year you'd have $8051.72 * 1.015 = $8172.50
And so on... (for five years)