In June 2027 the son-eomneun days fall on 3, 4, 13, 14, 23, 24. 6 in all. These are days whose lunar date ends in 9 or 0 — long the first thing people check before moving house or opening a shop.
June 6: 현충일. Taken from Korea Astronomy and Space Science Institute open data.
June 6: 망종; June 21: 하지. Computed from the sun's ecliptic longitude, not looked up in a table.
These dates hold for every visitor. A son-eomneun day is fixed by the lunar calendar alone and has nothing to do with your birth chart. What a given day means for you needs a birth date — there is no auspicious day that holds for everybody.