Case 1: Automatically merge all small polygons into a big one with respect to a specified attribute.
We can refer to the dissolve function in ArcToolbox.
Case 2: If the two specific polygons are expected to merge, follow the steps as follows
a. Select Editor > Start Editing.
b. Toggle the original polygon layer invisible.
c. Select the polygon features from the new polygon layer to be merged.
d. Select Editor > Merge.
e. The Merge dialog lists the polygon features to be merged. Click OK to merge the polygons features.
f. Select Editor > Stop Editing and click Yes to save the edits.
For more info, we can refer to the ESRI website
The dissolve function in ArcGIS 9.2 is not as capable as it was in Arcview 3.2. The dissolve function can experience memory limitation difficulty once the shapefile is too big. The workaround for the polygon dissolving is the usage of Arcview 3.2 geoprocessing wizard.