The interior angles of a triangle are 2 a  – 3 b , 4 a  –  b , and 6 a  + 4 b  where  a  and  b  are positive integers.

If the measure of the smallest angle is 24 ° , then what is the measure of the greatest angle?

Here interior angles of triangle are $2a-3b ; 4a-b \mathrm{and} 6a+4b$.
And we know that the sum of measures of triangle is $180°$. so we have;
 $$\begin{gathered} 2a-3b+4a-b+6a+4b = 180 \\ \Rightarrow 12a = 180 \\ \Rightarrow a = \frac{180}{12} = 15 \end{gathered}$$
Now putting a = 15 in all three angles we have;
$30-3b; 60-b \mathrm{and} 90+4b$
So here the measure of smallest angle is 30 - 3b and the measure of the greatest angle is 90 + 4b
 $$\begin{gathered} \mathrm{So}, 30-3b = 24 \\ \Rightarrow -3b = -6 \\ \Rightarrow b = 2 \end{gathered}$$
Therefore, the measure of the greatest angle = $90+4\times 2 = 98°$