Well done G-EMMA. Just one minor addition. Every "BECMG" and "TEMPO" group supersedes the previous, and in most cases the PROB groups will be aligned with the timing of the BECMG and TEMPO groups so they also supersede the previous.
So if you want to break it down into multiple paragraphs, here's how to do that:
EGNM 061516Z 061601 15010KT 9999 SCT020 <- The general overall picture at the start of the period, so at 16Z. Anything in here that's not superseded later on will remain valid throughout the period.
TEMPO 1620 7000 SHRA BKN010TCU <- Temporary condition between 16Z and 20Z, after which, if nothing else mentioned, it reverts back to 15010KT 9999 SCT020
PROB30 TEMPO 1620 4000 +SHRA +TSRA BKN008CB <- But within this same period it might get worse.
BECMG 1720 24006KT <- Ah, between 17Z and 20Z the wind will become 240/6. But for the rest the previous still applies. So theoretically, if the forecast holds true, at 20Z the conditions are 24006KT 9999 SCT020
BECMG 2023 7000 BKN008 <- And this is what's going to get established from 20Z to 23Z. So at 23Z the conditions should be 24006KT 7000 BKN008.
TEMPO 2301 3000 BR BKN003 <- And from 23Z onwards it will worsen once again.
Oh, and all times are UTC, not local.