Build the Service Layer

public class AccountHealthService {
    public Integer getOpenCaseCount(Id accountId) {
        return [SELECT COUNT() FROM Case WHERE AccountId = :accountId AND IsClosed = false];
    }

    public Decimal getAverageResolutionDays(Id accountId) {
        List<Case> closedCases = [
            SELECT CreatedDate, ClosedDate FROM Case
            WHERE AccountId = :accountId AND IsClosed = true AND ClosedDate != null
        ];

        if (closedCases.isEmpty()) {
            return 0;
        }

        Integer totalDays = 0;
        for (Case c : closedCases) {
            totalDays += c.CreatedDate.date().daysBetween(c.ClosedDate.date());
        }
        return totalDays / (Decimal) closedCases.size();
    }
}

getOpenCaseCount uses Module 20's COUNT() directly; getAverageResolutionDays computes the average in Apex since it needs a date difference SOQL's AVG() alone can't express — both handle the empty-data case (Module 17's "Handle Edge Cases" habit) up front.

public class AccountHealthSummary {
    public Integer openCaseCount;
    public Decimal averageResolutionDays;
    public Decimal totalWonRevenue;
    public Integer daysSinceLastActivity;
}

public AccountHealthSummary getHealthSummary(Id accountId) {
    AccountHealthSummary summary = new AccountHealthSummary();
    summary.openCaseCount = getOpenCaseCount(accountId);
    summary.averageResolutionDays = getAverageResolutionDays(accountId);
    summary.totalWonRevenue = getTotalWonRevenue(accountId);
    summary.daysSinceLastActivity = getDaysSinceLastActivity(accountId);
    return summary;
}

This is Module 34's DTO/wrapper-class pattern, used here at the service layer rather than directly in the controller — AccountHealthSummary doesn't yet have any @AuraEnabled annotations, since this class has no idea an LWC will ever use it (that's the controller's job, in a later lesson).

AccountHealthService and AccountHealthSummary could be called from an LWC controller, a batch job, or a plain Execute Anonymous script equally easily — nothing here mentions @AuraEnabled, cacheable, or anything LWC-specific. This mirrors Module 26's AccountRollupService: the logic that computes something and the logic that exposes it to a UI are deliberately kept as separate concerns.