To solve this equation, we need to first find the value of x in the first equation.

Given: 581 : 83 + 51 : x = 24.

This can be rewritten as: (581/83) + (51/x) = 24.

Now, we solve for x:

(581/83) + (51/x) = 24
=> (581/83) + (51/x) = 24
=> 7 + (51/x) = 24
=> 51/x = 17
=> x = 51/17
=> x = 3

Now that we have the value of x, we can substitute it into the second equation and solve for the value of x:

216/x + 16*18 = 324
=> 216/3 + 288 = 324
=> 72 + 288 = 324
=> 360 = 324

Therefore, the solution to the equation 216/x + 16*18 = 324 is x = 3.