1. **State the problem:** Simplify the algebraic expression $$4 + 6x - 5x + 4x$$. 2. **Identify like terms:** Like terms are terms that have the same variable raised to the same power. Here, the terms with $$x$$ are $$6x$$, $$-5x$$, and $$4x$$. The constant term is $$4$$. 3. **Combine like terms:** Add the coefficients of the $$x$$ terms: $$6x - 5x + 4x = (6 - 5 + 4)x = 5x$$ 4. **Write the simplified expression:** Combine the constant term and the simplified $$x$$ term: $$4 + 5x$$ 5. **Final answer:** The fully simplified expression is $$4 + 5x$$.