We start by determining the total amount of work done by the painting team. The work can be quantified in terms of member-minutes, where one member working for one minute contributes one unit of work.
Given that 12 members can complete the painting of a wall in 12 minutes, we can calculate the total work done in terms of member-minutes:
\[ \text{Total Work} = \text{Number of Members} \times \text{Time} = 12 , \text{members} \times 12 , \text{minutes} = 144 , \text{member-minutes} \]
Now, we want to find out how long it would take for 18 members to finish the same wall, which still requires a total of 144 member-minutes of work.
Let \( t \) be the time in minutes it takes for 18 members to paint the wall. The total work done by 18 members in \( t \) minutes can be expressed as:
\[ \text{Total Work} = 18 , \text{members} \times t , \text{minutes} = 18t , \text{member-minutes} \]
Since the total work required is the same (144 member-minutes), we set up the equation:
\[ 18t = 144 \]
Next, we solve for \( t \):
\[ t = \frac{144}{18} \]
Calculating the right-hand side:
\[ t = 8 \]
Thus, it would take 18 members 8 minutes to paint the wall. The final answer is:
\[ \boxed{8} \]