自慢: a source of pride or an act of showing off
Distinguish pride in a grandmother's cooking from a brother showing off his bicycle to friends, identifying the object and any stated audience.
Something the family takes pride in
自慢 (じまん) can mean pride or a boast. “祖母の手料理は家族みんなの自慢だ。” says that the grandmother's cooking is the pride of the whole family.
家族みんなの identifies who takes pride in it. The object of pride is her cooking; the sentence itself does not report the family boasting to a particular audience.
Showing a bicycle off to friends
“弟は新しい自転車を友達に自慢した。” says that the younger brother showed off his new bicycle to his friends. 新しい自転車 identifies what he showed off, and 友達に identifies the audience.
自慢した reports an act of showing off. Compared with 自慢だ as an evaluation of something, it distinguishes a source of pride from an action directed toward others.
Distinguish an evaluation from an action
The same 自慢 appears in a relationship of pride in cooking and an act of boasting about a bicycle. Read the surrounding expression and whether an audience is supplied.
Do not make 自慢 always mean an unfavorable exaggeration. A source of pride does not establish an act of boasting, and the bicycle example does not state how the friends reacted.
How does the family's 自慢だ differ from 自慢した to friends?
Show the answer and why
The first evaluates the grandmother's cooking as a source of pride for the family. The second reports the younger brother showing off his new bicycle to friends, with both the object and the audience stated.