If a molecule has 6 protons, 8 neutrons, and 7 electrons. What is the "nuclear" charge of the molecule

Answer 1

6 protons tells us the element is carbon (C)

8 neutrons tells us the atomic mass is 14, so this is the C-14 isotope

7 electrons tells us there is 1 more electron than protons, so the charge on the ion is 1-.

Now, the question is "are you asking about the effective nuclear charge", or just the charge in the nucleus?

And btw, this is not a molecule, as suggested in your question.

At any rate, the charge in the nucleus (without considering additional subatomic particles) is 6+.

The effective nuclear charge on the outer-most electron would be approximately 4+ (actually 3.14+)