Maybe you bought a cheap Chinese copy of an LM338 from fleabay?
Here is how a real LM338 works:

 

Measure the voltage at all three terminals for no load and loaded conditions.

No load:
High side of R1 = 5.76 Low side of R1 = 4.53
With load:
High side of R1 = 6.06 Low side of R1 = 4.84
With load:
High side of R2 = 4.84 junction of 220 Ohms resistors = 2.55
No load:
High side of R2 = 4.53 junction = 2.26

 

Reformatted for easier comparison:

No load:
OUT=5.76V, ADJ=4.53F, IN=?, VREF=1.23V
High side of R1 = 5.76 Low side of R1 = 4.53
High side of R2 = 4.53 junction = 2.26

With load:
OUT=6.06V, ADJ=4.84V, IN=?, VREF=1.22V
High side of R1 = 6.06 Low side of R1 = 4.84
High side of R2 = 4.84 junction of 220 Ohms resistors = 2.55

Still not making sense.

What is the input voltage for the above conditions?

 

Reformatted for easier comparison:
Still not making sense.

What is the input voltage for the above conditions?

12.6

 

It is confusing because he does not show a schematic with the value of R1 (probably 120 ohms).
I am guessing that for R2 he has two 220 ohm resistors in series.
We do not know if he has the important input and output capacitors and their type and values.

All these important details would be shown on a schematic.

 

It is confusing because he does not show a schematic with the value of R1 (probably 120 ohms).
I am guessing that for R2 he has two 220 ohm resistors in series.
We do not know if he has the important input and output capacitors and their type and values.

All these important details would be shown on a schematic.

The schematic I posted is a data sheet.
I built the circuit shown. It works very well.
The output capacitor is for voltages over 25 and a 10 microFarad Tantalum is required.
The input capacitor is only used if the input feed is more than 6 inches away from the input pin.

 

The schematic I posted is a data sheet.
I built the circuit shown. It works very well.
The output capacitor is for voltages over 25 and a 10 microFarad Tantalum is required.
The input capacitor is only used if the input feed is more than 6 inches away from the input pin.

Everything is fine but:
You agree on:

R2 = 440 Ohms.

And you insist in having R2 = 39+39 ohms.

Better, reread Audioguru's #21.

Every time I had problems with suspicious 3-pins voltage regulators circuits, I reassembled the whole circuit from scratch.

Do de same; throw it out of the window and start afresh.

Stop confusing the public and yourself.

 

Everything is fine but:
You agree on:


And you insist in having R2 = 39+39 ohms.

Better, reread Audioguru's #21.

Every time I had problems with suspicious 3-pins voltage regulators circuits, I reassembled the whole circuit from scratch.

Do de same; throw it out of the window and start afresh.

Stop confusing the public and yourself.

I used the two 220 Ohms in series.
I mentioned I found an error in my E/I calculation for R2.
Circuit works fine.