Comparing (1) and (2), we notice that

a = d

And comparing (1) and (3), we also notice that

c = b + 5

Armed with this new info, let's play with (4). Substitute a with d and c with b + 5. We'd have:

b + 5 - a = 6

Subtract 5 from both sides to eliminate 5 from the left hand side. It becomes:

b - a = 1

-a + b = 1 .................. (5)

Recall

a + b = 8 .................. (1)

Now we see that (5) has the same variables as (1) so eliminate one variable. If you add both equations, you'd eliminate a, but if you subtract, b goes. Let's add.

-a + a + b + b = 1 + 8

0 + 2b = 9

b = 4.5

but a + b = 8

Therefore

a = 8 - b = 8 - 4.5 = 3.5

d = a = 3.5

Then

c - d = 6

c - 3.5 = 6

c = 6 + 3.5 = 9.5