Kristin,Your question is a little ambiguous.
Do you want one 3/8 measure in one staff to have same duration as one 2/4 in the other staff (= "Multiple time signatures")?
Or do you want an 8th to have same duration in both staves (= "Independent barlines")? In the latter case 4 measures of 3/8 will have the same duration as 3 measures of 2/4.
Look in the documentation under "Multiple time signatures".
In short, this is the way for "Multiple time signatures":
Staff Tool
Double-click the second staff. The Staff Attributes dialog box appears.
In the pane "Independent Elements" check "Time Signature". Click OK.
Switch to Time Signature Tool, click the first staff and set it to 3/8, click the second staff and set it to 2/4.
For "Independent barlines" the situation is more tricky.
Basically you can't get independent barlines in Finale.
But if you are willing to do some work you can make a cheat that looks like independent barlines.
One way is setting the first 6 measures to 3/8, 1/8, 1/4, 1/4, 1/8 and 3/8. In the Time Signature dialog box you can click the "More Choices" button and set all measures in staff 1 to display 3/8, whereas all measures in staff 2 should display 2/4. In the Measure Attributes dialog box you can make the barlines invisible in those measures where the barline shouldn't go down through the score (measures 1 through 5 in this case).
The missing barlines can be inserted as expressions. The barline character has number 92 in the Maestro font. Assuming that you have set the number of beats to 1 in all measures, the barline character should be assigned to beat 2 (= the beat after the last beat) in order to be positioned at the right end of the measure. The vertical position should be -24 points.
This was the easy part. The hard part is the beaming. You probably already know that you can break/join beams with / in the Speedy Entry Tool. Read the documentation about "Beaming across barlines".
Another way is setting the time signature to 3/2 (Number of beats: 1; Beat duration: dotted whole note). You can avoid the "Beaming across barline" trouble in this way, but you may get trouble with the horizontal position of the false barlines.
Peter