If I play Rumble, if opponent asks me how many might I have on a battlefield, do I have to tell him with or without apply of shield?

You must give them the unit's current Might — which, outside of combat, is without Shield. Shield is "While I am a defender, I have +X Might" (Rule 814.1.c), so it only adds to Might when the unit actually has the Defender designation. A unit sitting on a battlefield isn't a defender, so its current Might is its printed Might plus any active modifiers (buffs, Assault if attacking, etc.).

Two layers here:

• Current Might is public information — you must answer honestly and accurately (Rule 502.4.d). Answering with Shield added while the unit isn't defending would be misrepresenting public information.
• What Shield would add if the unit became a defender is derived information — you're not required to compute or volunteer that future consequence (Rule 502.5.c; Rule 502.2.b). So you can answer "4 Might" and leave it at that.

If combat is already staged and the unit is actually a defender, then Shield is included in its current Might, and that's the number you report.