The single most important detail in this question is the type of the outcome variable. The disease is recorded simply as present or absent, which makes it a binary categorical outcome, and there are five candidate predictors.
The selection of a statistical model follows a simple rule based on the outcome. A continuous outcome with several predictors calls for multiple linear regression; a binary outcome with several predictors calls for multiple logistic regression. Because the disease state here is dichotomous, logistic regression is the technique that fits, and it conveniently reports adjusted odds ratios for each of the five factors.
Checking the other options confirms this. Multiple linear regression requires a numeric, continuous dependent variable and is therefore inappropriate for a yes or no outcome. ANOVA tests whether the means of a continuous variable differ between groups, again the wrong setting. The Kruskal-Wallis test is the non-parametric counterpart of one-way ANOVA for comparing more than two groups and is not a multivariable predictor model.
Note that the printed key labels multiple linear regression as the answer, but this is a known error in the recall paper. Linear regression cannot model a binary disease outcome, so the statistically valid answer is multiple logistic regression.
\[\boxed{\text{Multiple logistic regression}}\]