1. We are asked to evaluate the integral $$\int \frac{e^{\sqrt{6y + 4}}}{\sqrt{6y + 4}} \, dy.$$\n\n2. To solve this, use the substitution method. Let $$u = \sqrt{6y + 4}.$$\n\n3. Then, $$u^2 = 6y + 4.$$\n\n4. Differentiate both sides with respect to $$y$$: $$2u \frac{du}{dy} = 6 \implies \frac{du}{dy} = \frac{6}{2u} = \frac{3}{u}.$$\n\n5. Rearranging, $$dy = \frac{u}{3} du.$$\n\n6. Substitute into the integral: $$\int \frac{e^u}{u} \cdot dy = \int \frac{e^u}{u} \cdot \frac{u}{3} du = \int \frac{e^u}{3} du = \frac{1}{3} \int e^u du.$$\n\n7. Integrate: $$\frac{1}{3} e^u + C.$$\n\n8. Substitute back $$u = \sqrt{6y + 4}$$ to get the final answer: $$\frac{1}{3} e^{\sqrt{6y + 4}} + C.$$