I have the two boys going in a North East direction. I think that they were with two girls. But I could be wrong on the direction because it doesn't make sense,  since there is no house in that direction and I have the two boys walking and then entering a house with the girls.  Since Leo is in one of the signs I think they went to a party. I have tried to do the distance but have failed miserably.

How was North East arrived at ? Using the 8th house ?
8th being the derived 2nd from the 7th ( 7+2=8)...

and what distance formula was applied ?

I used the grouping of the most planets in a sign as per;

Direction is not always so obvious, in part because of the frequency of having mixed indicators. The general idea is this: take the major Significators in the chart. Examine their location by sign and by house. If the bulk of the planets are either in one house or one sign, then you can translate this into compass location using the cardinal points of the chart,: the Ascendant as East, etc.
I used the two finger method for distance, two fingers in the sky for two miles, North East?

Hummm - I guess this is where the discussion
gains from elucidation...

I always had the idea that perhaps some charts
one cannot get the ruler due to lack of the
astrologer understanding the query related
to the chart. In that case one would use
what ? I was considering just searching
in the direction ( and the reverse direction ) of
each ruler sequentially - as enclosed..

Most of the rulers are in the South West quadrant
so reversed would be North East - The reversal is
a possiblity but usually I only use this after a very
thorough search of the indicated direction.. but seems
okay - a congruent result but by differing logic.

I am not sure I understand the reasoning with the
two fingers... sort of astronomy I guess :)

I use the North latitude ( which Mercury is in ) to
get the multiplier of the angular distance in degrees
between the significator ( Mercury ) and the Moon.
About 65 degrees and the multiplier for North Latitudes
in Succedent house is 2 miles .. 2 miles by 65 degrees
is 130 miles. Astrology loves mixing units :)


The idea being if you lay the Locality chart over the
original position - and go either one way or the other
along the direction either toward or away from but
in the same straight line then in this case you get
South West or North East you get to the "lost article".

There are other approaches to this issue though :)
especially if the natal charts are available...

Interesting that in addition to the locality chart
if we take Mercury in Virgo - that by Sign gives
South by West. The concept being to get direction
go by Sign and then when at the distance
described by the chart - go by house - by
house is 8th west by south...

Still relatively in agreement with the Locality chart.