Standard calculation for Perimeter is 2L+2W=P or 2(L+W)=P
As we have the totals for the perimeter at 32m and know the lenght is 6m longer than width we can build an equation to find W.
2(L+W)=Perimeter
2(x+x+6)=32
2(2x+6)=32
2x+6=32/2
2x+6=16
2x=16-6
2x=10
x=10/2
x=5
Now we have the width of 5m. As length is 6m longer than width means we add 6m to 5m to determine length
L=W+6
L=5+6
L=11
To determine if your calculations are correct place your L and W answers into original eqution to determine perimeter
2(11+5)=32
2(16)=32
32=32
Yes, it is found correct. Now to find the Area using the standard formula for Area. Area=L*W or A=LW
A=(11)(5)
A=55
Area = 55sq m