Variables:
A = Number of adult tickets
S = Number of student tickets
318 = A + S : 318 (total number of tickets sold) = A (Number of adult tickets) + S (Number of student tickets)
A = 6 + 3 * S : A (The number of adult tickets) = 6 (was 6 more than) + 3 * S (3 times the number of student tickets)
We can replace A in the top equation in terms of S.
318 = (6 + 3*S) + S
318 = 6 + 4 * S
312 = 4 * S
78 = S
And to solve for A...
318 = A + 78
240 = A
We can double check by looking at our second equation
240 = 6 + 3 * 78
240 = 240