Certo, não consegui testar este caixa eletrônico, mas faria algo assim:
SELECT
proj_id,
project_estimates.Q1,
project_estimates.Q2,
project_estimates.Q3,
project_estimates.Q4,
project_expenditure.Q1,
project_expenditure.Q2,
project_expenditure.Q3,
project_expenditure.Q4
FROM projects
LEFT JOIN project_estimates ON (project_estimates.proj_id = projects.proj_id)
LEFT JOIN project_expenditure ON (project_expenditure.proj_id = projects.proj_id)
WHERE projects.proj_id IN (
(SELECT proj_id FROM project_estimates WHERE (project_estimates.fy = '2015-16'))
UNION
(SELECT proj_id FROM project_expenditure WHERE (project_expenditure.fy = '2015-16'))
GROUP BY proj_id
)
ORDER BY proj_id
