For when we were in the flesh, the passions of sins which were through the Law did work in our members to bring forth fruit unto death. In the flesh, to which might be opposed in the Spirit (cf. Romans 8:9), denotes our state when under the power of sin, before we had risen to a new life in Christ; it is virtually the same as what is meant by being under the Law, as is shown by the opposed expression in Romans 7:6, κατηργήθημεν ἀπὸ τοῦ νόμου.
What is signified by "the passions of sins" being "through the Law" will be considered under Romans 7:7 and Romans 7:8.