The most common and most likely answer to this crossword clue is the 4 plus 8 letter word WEAR BLINKERS
I've seen this crossword clue in Financial Times
W
E
A
R
B
L
I
N
K
E
R
S
Buddy explains!
The straight part
We know that "how to miss the big picture" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case how to miss the big picture = wear blinkers.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.