This is the 6170th most frequent Russian word.
твердо
Firmly; solidly.
In this sentence, 'твердым' describes 'намерением', emphasizing the determination of her intention.
Она работает над проектом с твердым намерением достичь успеха.
She works on the project with a firm intention to succeed.
Here, 'твердо' modifies the verb 'уверен', indicating the manner of the confidence.
Он твердо уверен в своём решении.
He is firmly confident in his decision.
Here, 'твердым' qualifies 'материалом', referring to the physical property of solidity.