6:22a For seven days they kept the Feast of Unleavened Bread with joy,

Then for seven days, they celebrated joyfully/happily the festival of Bread Without Yeast.
-or-
During the seven days ⌊after the Death Passed Us By feast⌋, they all celebrated the feast when we eat bread made without yeast.

6:22b because the LORD had made them joyful and turned the heart of the king of Assyria toward them

Yahweh had given them reason to be happy/joyful. He had changed the mind/heart/thoughts of the king of Assyria ⌊towards them ⌋.
-or-
They had great joy when they celebrated because Yahweh had caused the king of Assyria to show favor to them.

6:22c to strengthen their hands in the work on the house of the God of Israel.

As a result, he helped/aided them in the work ⌊of building⌋ the temple for the God of Israel.
-or-
He supported them as they built the house of God, the God ⌊that the people⌋ of Israel ⌊worship⌋.

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