I added a call to mysqli_fetch_assoc($showexpenses)to make it fully functional.
I also sanitized $project_id to avoid injections and used an alias to make the sum accessible through an associative array.
$getexpenses = "SELECT SUM(`expense_amount`) as `sum_amount` FROM `projects_expense` WHERE `project_id`= ".intval($project_id);
$showexpenses = mysqli_query ($dbc, $getexpenses);
$sums = mysqli_fetch_assoc($showexpenses);
$sum = $sums['sum_amount'];
echo $sum;
We could also have used mysqli_fetch_row like this:
$getexpenses = "SELECT SUM(`expense_amount`) FROM `projects_expense` WHERE `project_id`= ".intval($project_id);
$showexpenses = mysqli_query ($dbc, $getexpenses);
$sums = mysqli_fetch_row($showexpenses);
$sum = $sums[0];
echo $sum;
The alias is not needed anymore since we know the first column (0) is a match.
NB: you probably also need to GROUP BY project_id if you want to use SUM()
mysqli_query()won't be very useful. You need to treat this with something likemysqli_fetch_assoc();