Is the monthly deduction of 4% of the salary by the Israeli Ministry of Education, with the addition of double the amount from the Ministry and the investment of the money, then its return after 6 years, permissible (halal)? And how can it be made permissible?

It is impermissible to give money to Jews for investment purposes because they use it in forbidden usury. They earn profits from it and involve you by deducting from what they give you. Even if it were assumed that they invest it in permissible ways, it is still impermissible to give them money because it constitutes a corrupt mudarabah (profit-sharing) due to the predetermined profit.

It is impermissible for a Muslim to be an employee of a hostile non-Muslim who is not under a covenant of security. A non-Muslim should not be enabled to employ a Muslim. If the employment involves something forbidden by Sharia, such as teaching music, the matter becomes even more prohibited. One must leave such work and seek another, and it is not permissible to remain in it except out of a recognized legitimate necessity.