To determine which reaction shows a chemical change producing a solid, we will examine each reaction step by step:
### Reaction A:
[tex]\[ 2 \text{CH}_3\text{OH} (l) + 3 \text{O}_2 (g) \rightarrow 2 \text{CO}_2 (g) + 4 \text{H}_2\text{O} (l) \][/tex]
In this reaction, methanol ([tex]\(\text{CH}_3\text{OH}\)[/tex]) and oxygen ([tex]\(\text{O}_2\)[/tex]) react to produce carbon dioxide ([tex]\(\text{CO}_2\)[/tex]) and water ([tex]\(\text{H}_2\text{O}\)[/tex]). All products and reactants are either gases or liquids. No solid is produced in this reaction.
### Reaction B:
[tex]\[ 2 \text{AgNO}_3 (aq) + \text{CaBr}_2 (aq) \rightarrow 2 \text{AgBr} (s) + \text{Ca(NO}_3\text{)}_2 (aq) \][/tex]
Here, aqueous solutions of silver nitrate ([tex]\(\text{AgNO}_3\)[/tex]) and calcium bromide ([tex]\(\text{CaBr}_2\)[/tex]) react to form silver bromide ([tex]\(\text{AgBr}\)[/tex]), which is a solid, and calcium nitrate ([tex]\(\text{Ca(NO}_3\text{)}_2\)[/tex]), which remains in aqueous solution. The formation of the solid silver bromide ([tex]\(\text{AgBr}\)[/tex]) indicates a chemical change producing a solid.
### Reaction C:
[tex]\[ \text{NaCl} (s) \rightarrow \text{NaCl} (aq) \][/tex]
In this reaction, sodium chloride ([tex]\(\text{NaCl}\)[/tex]) dissolves in water, changing from a solid to an aqueous state. There is no new solid product formed; rather, the existing solid dissolves.
### Reaction D:
[tex]\[ \text{H}_2 (g) + \text{O}_2 (g) \rightarrow \text{H}_2\text{O} (g) \][/tex]
Hydrogen ([tex]\(\text{H}_2\)[/tex]) and oxygen ([tex]\(\text{O}_2\)[/tex]) react to form water vapor ([tex]\(\text{H}_2\text{O}\)[/tex]). All reactants and products are in the gaseous state. No solid is produced in this reaction.
### Conclusion
Given the analysis above, the reaction that shows a chemical change producing a solid is:
[tex]\[ B. \ 2 \text{AgNO}_3 (aq) + \text{CaBr}_2 (aq) \rightarrow 2 \text{AgBr} (s) + \text{Ca(NO}_3\text{)}_2 (aq) \][/tex]
Therefore, the correct answer is:
[tex]\[ \boxed{2} \][/tex]
