It may be the case that 60% of the tickets sold are for adults (eg 40 tickets sold to children and 60 tickets sold to adults), but this does NOT mean that the cost of all the adult tickets is 60% of the total cost of the tickets sold.

When you wrote 60/100 x 6720, you are assuming that the cost of adult tickets sold is 60% of the total cost.

Alternative to AC's method :

Since 40% of tickets sold are child tickets,
and 40% = 2/5, 60% (or 3/5) of tickets sold are adult tickets.

This means for every 2 child tickets sold, there were 3 adult tickets sold.

Group 2 child tickets and 3 adult tickets into a set.

Price of tickets in 1 set
= 2 x $7 + 3 x $14
= $14 + $42
= $56

Number of sets
= $6720 ÷ $56
= 120

Number of adult tickets sold
= 3 per set x 120 sets
= 360

Second alternative : Price x quantity.

Since child tickets cost 50% less than adult tickets,

Ratio of price of child tickets to price of adult tickets = 1 : 2

Since 40% = 2/5, Ratio of number of child tickets sold to adult tickets sold

= 2 : 3

Ratio of the total cost of the children tickets to the adult tickets

= (1 x 2) : (2 x 3)
= 2 : 6
= 1 : 3

That's a total of 4 units.

4 units = $6720
Total cost of adult tickets= $6720 x ¾
= $5040

Number of adult tickets sold
= $5040 ÷ $14 per ticket
= 360