Since you post in ,NET forum, I assume you are asking for programmingly open AutoCAD's built-in Text Style dialog box. The dialog box itself is not exposed via .NET API, but yes, you can use Document.SendStringToExecute() to open it:
[CommandMethod("OpenStyle")] public static void OpenTextStyleDialogBox() { Document dwg = Application.DocumentManager.MdiActiveDocument; dwg.SendStringToExecute("._STYLE ", true, false, true); }
However, due to the nature of SendStringToExecute(), you do not place more code following the SendStringToExecute() with which the execution depends on the user interaction with the dialog box.
If you have to do something accordingly based on what user does with the dialog box, you may want to look into handling CommandWillStart and/or CommandEnded.
As an alternative, you may simply create your own simplified Text Style dialog box, so taht you have full control to the workflow.