What you need to do is to extend those roof shingles into the gutter.
How shingles overlap gutter.
If you have a straight run gable roof measure from shingle to shingle and then add 1 2 inch to each side for a slight overlap.
In many cases and particularly as home ages and settles the roof edge at the eave edge can wave in and out by more than this amount.
Gutters should be hung where a straight edge laying on your roof shingles can easily extend over the front lip of the gutter this is the proper installment location for the high point of the gutter.
If there s a drip edge installed where the fascia meets your shingles and the gutter is hung below the drip edge get some roll flashing and tuck it up under the drip edge and over the top of the gutter.
Longer overlaps of asphalt shingles past the drip edge will hang over into the gutter will send roof runoff off of the roof rather than into the gutter and will eventually crack break and look gross.
This will leave room for the inside box miter.
The drip edge flashing you depicted is called t drip style or o d e which stands for overhanging drip edge.
When it rains hard the water running down my roof will run right past the gutter and onto the ground.
In my opinion the shingles should never be exactly even with the edge of any drip edge flashing.
If you have inside corners subtract 5 inches.
Shingles hang over gutter.
And you re going to slip underneath some flashing.
To this total length add 4 more inches to the length this is for an overlap at the interior joined seam it will make the gutter stronger in that area.
Measure the total run of the gutter length you need.
For outside corners measure from corner to corner.
Home centers sell rolls of 6 in.
So because there s not a magic potion that will do that the way to fix this is to get a flat bar and that s a very thin pry bar.
Use tin snips to cut the gutter apron flashing roll in two 3 in.
Each has their own reasoning for a slightly different amount of overhang.
And you re lifting up the edges of those shingles at the bottom of the roof edge.
The shingles appear to have been installed such that they cover almost half of the gutter.
See overshooting gutters just below we illustrate shingles installed with too much overhang into the gutter.