If A is the number of adults, then there are 9-A children.
Each adult eats 4 pancakes, so they eat 4A pancakes between them.
The children eat 9(9-A) pancakes between them.
So the total number of pancakes eaten is 4A+9(9-A)=51.
Therefore, 4A+81-9A=51, 5A=81-51=30, so A=30/5=6, there are 6 adults.