1. **State the problem:** Solve for $w$ in the equation $13w - 10w = 6$. 2. **Combine like terms:** Since both terms on the left side contain $w$, subtract the coefficients: $$13w - 10w = (13 - 10)w = 3w$$ So the equation becomes: $$3w = 6$$ 3. **Isolate $w$:** To solve for $w$, divide both sides of the equation by 3: $$\frac{3w}{\cancel{3}} = \frac{6}{\cancel{3}}$$ which simplifies to: $$w = 2$$ 4. **Final answer:** The value of $w$ that satisfies the equation is: $$\boxed{2}$$