We need a number that has remainder $4$ when divided by $6$ and remainder $5$ when divided by $7$.

Numbers with remainder $4$ when divided by $6$: $4, 10, 16, 22, 28, 34, 40, \ldots$

Check each for remainder $5$ when divided by $7$:

• $4 \div 7 = 0$ R $4$ $\times$
• $10 \div 7 = 1$ R $3$ $\times$
• $16 \div 7 = 2$ R $2$ $\times$
• $22 \div 7 = 3$ R $1$ $\times$
• $28 \div 7 = 4$ R $0$ $\times$
• $34 \div 7 = 4$ R $6$ $\times$
• $40 \div 7 = 5$ R $5$ $\checkmark$

The answer is $40$.