So, Toshihiko's answer gives the answer for the normal case, but there is a whole other facet of this issue:
Do two nouns always compound or not?
And the answer is that in many cases they do not. I can't list out all the cases, but the major categories to pay close attention to are:
1. N2 is somehow locative
E.g.,
- ロシア南部 → ロ＼シア・ナ＼ンブ
- ロシア国境 → ロ＼シア・コッキョー￣
- ヨーロッパ各国 → ヨーロ＼ッパ・カ＼ッコク
You may occasionally hear the compounded versions of these, but not-compounded is more common.
2. N2 is a transitive suru-verb (他サ)
subject+verb → no compounding
object+verb → compounding
結果発表 → ケッカハ＼ッピョー
乱数調整 → ランスーチョ＼ーセー
再建検討 → サイケンケ＼ントー
承認申請 → ショーニンシ＼ンセー
自動車販売 → ジドーシャハ＼ンバイ
※ However, there are some exceptions like 〜禁止 (perhaps it's more of a
shortening than 〜が禁止だ or 〜が禁止されている as opposed to 〜を禁止する):
- タバコ禁止 → タバコ￣・キンシ￣
- 撮影禁止 → サツエー￣・キンシ￣
Other exceptions: 〜中止、〜防止、〜改正、〜独占
modifier+verb → compounding
- 急激上昇 → キューゲキジョ＼ーショー
- 全国販売 → ゼンコクハ＼ンバイ
3. N2 is an intransitive suru-verb (自サ)
subject+verb → no compounding
- 雨雲発達 → アマグモ￣・ハッタツ￣
- 社長辞任 → シャチョー￣・ジニン￣
- 景気後退 → ケーキ￣・コータイ￣
modifier+verb → compounding
- 一時帰国 → イチジキ＼コク
- 引責辞任 → インセキジ＼ニン
4. N2 is a both transitive and intransitive suru-verb (自他サ)
subject/object+verb → no compounding (usually, especially when it's a novel combination)
- 所得減少 → ショトク￣・ゲンショー￣ (or ショ＼トク・ゲンショー￣）
- 問題解決 → モンダイ￣・カイケツ￣ (* see below)
- 感染拡大 → カンセン￣・カクダイ￣ (* see below)
But it seems like if they get lexicalized enough they can compound:
- 人口減少 → ジンコーゲ＼ンショー (I think this is always compounded)
- 問題解決 → モンダイカ＼イケツ (I list this in both sections because you hear both)
- 感染拡大 → カンセンカ＼クダイ (You used to hear this more but it seems like everyone has settled on not compounding it)
modifier+verb → compounding
