1. Problem: Solve the literal equation $$\frac{2b}{3g} = \frac{s}{4t}$$ for $$t$$. 2. Formula and rules: To solve for $$t$$, we want to isolate $$t$$ on one side of the equation. We can do this by cross-multiplying and then dividing. 3. Cross-multiply: $$2b \cdot 4t = 3g \cdot s$$ 4. Simplify: $$8bt = 3gs$$ 5. Divide both sides by $$8b$$ to isolate $$t$$: $$t = \frac{3gs}{\cancel{8b}} \cdot \frac{\cancel{1}}{1} = \frac{3gs}{8b}$$ 6. Final answer: $$t = \frac{3gs}{8b}$$ This means $$t$$ is equal to $$3gs$$ divided by $$8b$$.