Aliasēt tabulas vajag:
SELECT
`studenti`.`name`,
`studenti`.`surname`,
`tests`.`atzime`,
`prieksmets1`.`nosaukums`, // vai arī prieksmets2, nezinu kuru tev tur vajag
`pasniedzeji`.`name_pas`,
`pasniedzeji`.`surname_pas`
FROM `tests`
INNER JOIN `studenti` ON (`studenti`.`id` = `tests`.`studenta_id`)
INNER JOIN `prieksmets` AS prieksmets1 ON (`prieksmets1`.`id` = `tests`.`prieksmeta_id`)
INNER JOIN `prieksmets` AS prieksmets2 ON (`prieksmets2`.`id` = `pasniedzejs_prieksmets`.`prieksmeta_id`)
INNER JOIN `pasniedzeji` ON (`pasniedzeji`.`id` = `pasniedzejs_prieksmets`.`pasniedzeja_id`)