The correct answer is   $180$ . Let  $a$ be the number of adult tickets sold and  $c$ be the number of child tickets sold. Since the theater sold a total of  $30$ tickets, $a+c=30$. The price per adult ticket is  $$12$, and the price per child ticket is  $$8$. Since the theater received a total of  $$300$  for the  $30$  tickets sold, it follows that  $12a+8c=300$. To eliminate $c$, the first be multiplied by  $8$ and then subtracted from the second equation:

$12a+8c=300$

$\dfrac{-8a-8c=-240}{4a+0c=60}$

 Because the question asks for the amount spent on adult tickets, which is   $12a$  dollars, the resulting equation can be multiplied by  $3$ to give  $3(4a)=3(60)=180$. Therefore, $$180$  was spent on adult tickets.

Alternate approach: If all the 30 tickets sold were child tickets, their total price would be   30(58)= \240$. Since the actual total price of the$30  tickets was  \$$300, the extra  $560$  indicates that a certain number of adult tickets, a, were sold. Since the price of each adult ticket is  $$4$  more than each child ticket, $4a=60$, and it follows that  $12a=180$.