The correct statement should be one in four homeless men are veterans. Most are sheltered (place to sleep at night, food provided).

Health care and job training was poor for veterans, particularly veterans of the Vietnam War.

About 40% of homeless are single men. Of these, 23% are veterans. One-fourth of 40% = 10%.
Add to this the male members, who were veterans, of the 40% of homeless who are families with children.

Most of these homeless are sheltered.

(Department of Housing and Urban Development Figures, summarized in Wikipedia, "Homelessness in the United States")