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MissPhiladelphia
The total atomic number must be the same on each side. The total mass number must be the same on both side. 

On the RHS, for the mass number, we have 257 + 4 = 261 (the 4 comes from the 4 neutrons). That means the mass number of the missing piece on the LHS is 261 - 247 = 14. 

One the RHS, for the atomic number we have a total of 104 since the 4 neutrons are all neutral. On the LHS, we have this: 104 - 98 = 6. 

The missing piece is a nucleus of carbon 14. Done in your style, it is 14/6C
Uraniumdavid

Answer: the missing nucleus is an isotope of oxygen 18/8 O

Explanation:

Since the reacting mass must be equal to the resulting mass

That is right hand side must be equal to the left

We check the total number of reacting moles in the equation

On the right hand we have 267/106

On the left hand side we have 249+x/98+x

Equation both we have

249+ x/98+y = 267/106

Therefore x = 18

y = 8

This is an isotope of oxygen

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