A ring of radius 0.30 m carries +12 nC spread evenly…

Step 1. The position. The field is greatest at $z = \dfrac{R}{\sqrt{2}} = \dfrac{0.30\ \text{m}}{1.414} = 0.212\ \text{m}$.

Step 2. The greatest field. $E_{\max} = \dfrac{2}{3\sqrt{3}}\,\dfrac{kQ}{R^2} = 0.385 \times 1200\ \text{N/C} = 462\ \text{N/C}$.

Step 3. At $z = R$. $E = \dfrac{kQR}{(2R^2)^{3/2}} = \dfrac{kQ}{2\sqrt{2}\,R^2} = \dfrac{1200}{2.828}\ \text{N/C} = 424\ \text{N/C}$.