Let \( a \) represent the number of true/false questions in Part A, and let \( b \) represent the number of multiple choice questions in Part B. The total points for Part A can be represented as:
\[ \text{Points for Part A} = 6a \]
And for Part B, the total points can be expressed as:
\[ \text{Points for Part B} = 4b \]
We know that the points for Part A and Part B are equal:
\[ 6a = 4b \]
To simplify this equation, we can divide both sides by 2:
\[ 3a = 2b \]
This can be rearranged to express \( b \) in terms of \( a \):
\[ b = \frac{3}{2}a \]
Since \( b \) must be a whole number (as it represents the number of questions), \( a \) must be even. Let \( a = 2k \) for some integer \( k \). Then we substitute into the equation for \( b \):
\[ b = \frac{3}{2}(2k) = 3k \]
Now substituting back to find the points, we calculate the total points for Part A and Part B. The points from Part A are:
\[ 6a = 6(2k) = 12k \]
The points from Part B are:
\[ 4b = 4(3k) = 12k \]
Both parts yield \( 12k \) points. To find the least number of points for which this is possible, we choose \( k = 1 \):
\[ \text{Points for each part} = 12(1) = 12 \]
Thus, both Part A and Part B are worth:
\[ \boxed{12} \text{ points} \]
To summarize, Part A has \( a = 2 \) true/false questions (worth \( 12 \) points total), and Part B has \( b = 3 \) multiple choice questions (also worth \( 12 \) points total).