Two protons are 2.0 × 10⁻¹⁵ m apart inside a nucleus…

Step 1. The electric force. $F_e = \dfrac{ke^2}{r^2}$. The top is $9.0 \times 10^9 \times (1.6 \times 10^{-19})^2\ \text{N m}^2 = 2.30 \times 10^{-28}\ \text{N m}^2$. The bottom is $(2.0 \times 10^{-15}\ \text{m})^2 = 4.0 \times 10^{-30}\ \text{m}^2$. So $F_e = 57.6\ \text{N}$.

Step 2. The force of gravity. $F_g = \dfrac{Gm_p^2}{r^2}$. The top is $6.67 \times 10^{-11} \times (1.67 \times 10^{-27})^2\ \text{N m}^2 = 1.86 \times 10^{-64}\ \text{N m}^2$. The bottom is $4.0 \times 10^{-30}\ \text{m}^2$, as before. So $F_g = 4.65 \times 10^{-35}\ \text{N}$.

Step 3. The ratio. $\dfrac{F_e}{F_g} = \dfrac{57.6\ \text{N}}{4.65 \times 10^{-35}\ \text{N}} = 1.24 \times 10^{36}$.

What does this mean? The protons push each other apart with $57.6$ N, a huge force for a particle. Gravity cannot hold them together. Another force, the strong nuclear force, must be much stronger still.