To determine which combination will make a basic buffer, we need to understand the concept of a buffer solution.$\\$A basic buffer is typically made by mixing a weak base with its conjugate acid.$\\$In this case, the weak base is $$NH$_4$OH (ammonium hydroxide), and its conjugate acid is $$NH$_4^+$ (from $$NH$_4$Cl).$\\$Let's analyze each option:$\\$Option 1: $50$ mL of $0.1$ M NaOH$+ 25$ mL of $0.1$ M CH$_3$COOH$\\$• This is a strong base (NaOH) with a weak acid (acetic acid). It will not form a buffer.$\\$Option 2: $100$ mL of $0.1$ M CH$_3$COOH$+ 100$ mL of $0.1$ M NaOH$\\$• This is a neutralization reaction between a weak acid and a strong base, resulting in a salt and water. No buffer is formed.$\\$Option 3: $100$ mL of $0.1$ M HCl$+ 200$ mL of $0.1$ M NH$_4$OH$\\$• Here, we have a weak base (NH$_4$OH) and its conjugate acid (NH$_4^+$ from the reaction with HCl). This will form a basic buffer.$\\$Option 4: $100$ mL of $0.1$ M HCl$+ 100$ mL of $0.1$ M NaOH$\\$• This is a neutralization reaction between a strong acid and a strong base, resulting in water and salt. No buffer is formed.$\\$Therefore, the correct option is Option 3, which forms a basic buffer.