What is the total future value six years from now of $80 received in
one year, $300 recceivedd in two years, and $700 received in six years
if the discount rate is 7%?

Draw a time line and layout your cash flows. I cant draw one here. But
you can see any text book on finance and see what i mean by a time
line (current year that is year 0 to final year that is year 5....
that's six years).

We are interested in knowing the value in year 5 according to our time
line that is the sixth year from now.

Cash received today or in year 0 (CF0)= 0
Cash received in one year from now (CF1)= 80
Cash received in two years from now (CF2)=300
Cash received in three years from now (CF3)=0
Similarly, CF4=0
and cash received in 6 years from now CF5=700

You earn interest for 4 years for cash received one year from now.
(Draw a time line numbered from 0 to 5....that's 6 years. Now, mark
the values for CF0 through CF5 on it.)

By definition, Future Value one year from now
= (Present Value x interest rate) + Present Value
= Present Value x (1+ interest rate)

So, for n years down the line,
Future Value=Present Value x (1+interest rate)^n

Hence,
Future Value (CF1) = 80 x (1+0.07)^4
Future Value (CF2)= 300 x (1+0.07)^3
Future Value (CF5)= 700 x (1+0.07)^0

Add the above future values and i guess you should have the answer.