Solution:

We can write that:

8! = 8 × 7 × 6!

7! = 7 × 6!

So by making use of these values,

$ 1/6!\text{ }+\text{ }1/7!\text{ }=\text{ }x/8! $

$ 1/6!\text{ }+\text{ }1/\left( 7\times 6! \right)\text{ }=\text{ }x/8! $

$ \left( 1\text{ }+\text{ }7 \right)/\left( 7\times 6! \right)\text{ }=\text{ }x/8! $

$ 8/7!\text{ }=\text{ }x/8! $

$ 8/7!\text{ }=\text{ }x/\left( 8\times 7! \right) $

$ x\text{ }=\text{ }\left( 8\text{ }\times \text{ }8\text{ }\times \text{ }7! \right)/7! $

$ x=\text{ }8\text{ }\times \text{ }8 $

$ x=\text{ }64 $

Therefore, the value of x is 64.